How to find comon patterns between different groups using R? - r

I have a data frame that indicates a road type and 24 columns (h_1 ... h_24) that show how many vehicles pass (relatively over the day) per hour. Each row is a different road.
I'm interested to find commonalities among types. My intended output is a condensation of the roadtypes. I.e. road type 2 and 3 appear to have the same pattern, so they are group into a new category (e.g. category).
So my question is, how can one detect this kind of pattern with as many as 15 different types?
Part of my data:
structure(list(type = c(14, 14, 11, 4, 13, 12, 13, 13, 13, 13,
11, 14, 1, 11, 14, 11, 4, 13, 14, 9, 14, 13, 13, 9, 14, 13, 1,
11, 14, 13, 13, 13, 11, 13, 15, 11, 14, 11, 14, 13, 9, 11, 13,
9, 14, 13, 13, 13, 13, 13, 9, 14, 13, 12, 11, 14, 11, 4, 11,
4, 13, 9, 13, 9, 13, 13, 1, 15, 1, 6, 13, 11, 13, 6, 11, 11,
11, 13, 13, 13, 12, 13, 14, 13, 11, 9, 14, 11, 13, 11, 3, 11,
11, 11, 14, 11, 13, 14, 13, 11, 11, 14, 11, 11, 13, 15, 12, 11,
4, 13, 14, 13, 11, 13, 14, 11, 9, 13, 13, 11, 11, 11, 13, 11,
11, 13, 13, 13, 14, 11, 9, 11, 13, 4, 12, 13, 13, 9, 13, 11,
13, 11, 13, 1, 9, 13, 11, 11, 13, 11), h_1 = c(1.091, 0.591,
1.129, 0.274, 0.178, 1.507, 0.654, 1.003, 0.228, 0.657, 1.411,
0.97, 0.875, 0.397, 1.462, 1.063, 0.648, 1.181, 0.629, 1.219,
2.193, 1.054, 0.768, 0.922, 1.525, 2.891, 0.888, 1.171, 0.684,
0.455, 0.562, 1.138, 0.895, 0.71, 0.445, 1.444, 3.644, 2.365,
0.391, 0.687, 1.037, 0.423, 2.14, 0.942, 1.33, 0.737, 1.766,
0.144, 1.08, 0.672, 0.629, 0.39, 0.325, 1.079, 2.099, 0.163,
0.871, 1.112, 1.731, 0.313, 1.039, 1.057, 1.159, 0.959, 0.755,
0.741, 0.429, 1.017, 0.602, 0.359, 0.574, 0.872, 0.639, 0.786,
0.857, 1.212, 2.553, 1.755, 0.543, 1.691, 0.715, 0.352, 1.431,
1.188, 2.115, 0.536, 0.605, 0.894, 0.745, 2.639, 0.545, 1.135,
0.702, 0.82, 0.462, 0.263, 1.362, 0.226, 0.801, 1.783, 1.301,
1.024, 1.394, 1.512, 1.151, 4.175, 0.644, 2.11, 0.518, 1.938,
1.048, 0.942, 1.233, 1.024, 1.967, 1.601, 0.736, 0.496, 1.346,
1.109, 0.78, 0.635, 0.567, 0.378, 2.976, 0.453, 0.392, 1.362,
1.042, 0.555, 1.218, 0.936, 1.098, 0.868, 1.172, 0.247, 1.287,
0.824, 1.025, 0.863, 1.484, 0.507, 1.335, 0.637, 1.986, 1.137,
0.837, 1.787, 0.353, 1.865), h_2 = c(0.607, 0.284, 0.753, 0.164,
0.085, 1.046, 0.422, 0.816, 0.1, 0.445, 1.032, 0.559, 0.699,
0.334, 1.092, 0.544, 0.494, 0.803, 0.251, 0.862, 2.53, 1.389,
0.705, 0.382, 0.932, 2.332, 0.604, 0.801, 0.329, 0.248, 0.411,
0.866, 0.584, 0.295, 0.26, 0.873, 2.943, 1.887, 0.287, 0.462,
0.668, 0.411, 2.101, 0.636, 0.88, 0.389, 1.24, 0.072, 0.804,
0.481, 0.346, 0.194, 0.093, 0.629, 1.644, 0.122, 0.615, 0.604,
1.308, 0.25, 0.577, 0.996, 0.849, 0.594, 0.418, 0.452, 0.252,
0.706, 0.348, 0.16, 0.297, 0.608, 0.57, 0.413, 0.745, 0.839,
1.894, 1.315, 0.344, 1.046, 0.35, 0.206, 0.987, 0.422, 1.595,
0.229, 0.263, 0.501, 0.556, 2.112, 0.303, 0.765, 0.485, 0.517,
0.24, 0.11, 0.88, 0.104, 0.649, 1.198, 0.948, 0.708, 0.917, 0.729,
0.743, 3.336, 0.35, 1.635, 0.253, 1.421, 0.539, 0.554, 0.82,
0.708, 1.411, 1.011, 0.638, 0.297, 0.918, 0.427, 0.676, 0.449,
0.556, 0.401, 2.192, 0.194, 0.264, 0.879, 0.667, 0.319, 0.854,
0.613, 0.683, 0.481, 0.855, 0.305, 0.865, 0.593, 0.568, 0.552,
1.002, 0.314, 0.953, 0.341, 1.415, 0.508, 0.441, 1.18, 0.24,
1.277), h_3 = c(0.505, 0.171, 0.277, 0.164, 0.097, 0.774, 0.305,
0.646, 0.132, 0.416, 0.853, 0.412, 0.621, 0.508, 0.8, 0.336,
0.432, 0.667, 0.163, 0.7, 2.953, 0.383, 0.656, 0.161, 0.635,
0.551, 0.466, 0.295, 0.229, 0.217, 0.141, 1.002, 0.498, 0.138,
0.177, 0.531, 1.688, 1.634, 0.259, 0.472, 0.565, 0.42, 2.051,
0.488, 0.703, 0.202, 1.03, 0.072, 0.603, 0.552, 0.208, 0.122,
0.023, 0.419, 1.278, 0.081, 0.54, 0.397, 0.921, 0.188, 0.357,
1.049, 0.602, 0.431, 0.193, 0.191, 0.204, 0.452, 0.3, 0.1, 0.173,
0.216, 0.531, 0.28, 0.772, 0.307, 1.486, 0.994, 0.164, 0.681,
0.229, 0.222, 0.723, 0.134, 1.217, 0.189, 0.152, 0.205, 0.562,
1.579, 0.242, 0.114, 0.434, 0.401, 0.218, 0.07, 0.645, 0.111,
0.604, 0.876, 0.847, 0.603, 0.797, 0.573, 0.464, 2.183, 0.266,
1.08, 0.161, 1.034, 0.342, 0.43, 0.533, 0.603, 1.064, 0.601,
0.731, 0.24, 0.801, 0.173, 0.192, 0.141, 0.522, 0.435, 1.044,
0.129, 0.226, 0.64, 0.502, 0.113, 0.466, 0.54, 0.523, 0.283,
0.697, 0.321, 0.701, 0.461, 0.358, 0.403, 0.828, 0.151, 0.662,
0.272, 0.997, 0.28, 0.195, 0.611, 0.353, 1.027), h_4 = c(0.366,
0.166, 0.218, 0.206, 0.047, 0.625, 0.333, 0.685, 0.691, 0.739,
0.937, 0.397, 0.739, 0.703, 0.737, 0.304, 0.432, 0.621, 0.163,
0.774, 2.831, 0.101, 0.929, 0.153, 0.466, 0.186, 0.454, 0.218,
0.331, 0.302, 0.105, 2.127, 0.638, 0.188, 0.264, 0.548, 1.327,
1.387, 0.394, 0.791, 0.614, 0.639, 1.671, 0.496, 1.185, 0.179,
1.192, 0.287, 0.779, 0.844, 0.265, 0.187, 0.023, 0.383, 1.169,
0.122, 0.764, 0.334, 0.835, 0.188, 0.367, 1.277, 0.799, 0.414,
0.193, 0.245, 0.3, 0.367, 0.363, 0.2, 0.254, 0.167, 0.574, 0.186,
1.166, 0.221, 1.512, 0.832, 0.161, 0.714, 0.326, 0.416, 0.867,
0.23, 1.107, 0.348, 0.218, 0.179, 0.935, 1.295, 0.262, 0.177,
0.823, 0.472, 0.295, 0.116, 0.717, 0.271, 0.791, 0.958, 1.371,
0.744, 0.968, 0.706, 0.409, 1.466, 0.249, 0.912, 0.207, 0.827,
0.332, 0.359, 0.702, 0.744, 0.859, 0.544, 0.993, 0.357, 1.109,
0.218, 0.299, 0.144, 0.558, 1.027, 0.761, 0.172, 0.349, 0.719,
0.664, 0.18, 0.406, 0.777, 0.541, 0.274, 0.918, 1.109, 0.675,
0.522, 0.321, 0.489, 0.828, 0.085, 0.57, 0.351, 0.823, 0.134,
0.215, 0.559, 0.396, 1.172), h_5 = c(0.759, 0.362, 0.394, 1.041,
0.08, 0.598, 0.714, 0.738, 4.113, 1.674, 0.948, 0.661, 1.051,
2.606, 0.996, 0.462, 0.571, 1.056, 0.415, 1.242, 2.291, 0.096,
1.211, 0.288, 0.593, 0.727, 0.721, 0.305, 0.967, 0.687, 0.257,
4.004, 1.267, 0.381, 0.628, 0.813, 1.521, 1.281, 0.925, 1.738,
0.872, 2.14, 1.936, 0.698, 1.752, 0.29, 2.07, 0.647, 1.381, 1.377,
0.531, 0.514, 0.162, 0.408, 1.346, 0.448, 2.163, 0.429, 0.907,
0.563, 0.499, 2.062, 1.532, 0.572, 0.396, 0.52, 0.754, 0.537,
0.714, 0.819, 0.821, 0.255, 0.836, 0.266, 2.112, 0.313, 2.199,
0.796, 0.367, 1.3, 0.544, 1.199, 1.131, 0.23, 1.134, 1.306, 0.417,
0.199, 1.416, 1.598, 0.545, 0.3, 2.043, 0.963, 0.652, 0.354,
1.26, 0.793, 1.481, 1.838, 3.07, 1.419, 1.634, 0.932, 0.39, 1.545,
0.701, 1.102, 0.46, 0.887, 0.585, 0.543, 0.999, 1.419, 1.107,
0.623, 1.456, 0.56, 1.963, 0.231, 0.439, 0.162, 0.784, 2.901,
1.314, 0.323, 0.847, 1.264, 1.313, 0.417, 0.78, 1.9, 0.857, 0.538,
1.647, 2.558, 1.153, 0.768, 0.568, 0.91, 1.421, 0.237, 0.755,
0.832, 1.183, 0.107, 0.491, 1.175, 0.848, 2.117), h_6 = c(1.836,
0.961, 1.605, 3.069, 0.089, 1.005, 2.508, 1.717, 5.413, 4.381,
1.665, 1.441, 1.89, 6.892, 2.116, 1.612, 1.157, 2.141, 1.571,
3.35, 2.667, 0.718, 1.845, 0.978, 1.186, 1.787, 1.974, 1.03,
2.14, 1.405, 1.073, 5.952, 3.467, 1.101, 1.578, 2.122, 2.36,
1.302, 2.865, 3.508, 1.718, 4.415, 2.705, 1.552, 3.541, 0.97,
3.108, 0.862, 3.365, 2.782, 1.806, 1.757, 2.921, 0.752, 2.146,
0.855, 4.545, 0.683, 1.447, 1.939, 1.292, 3.794, 3.581, 1.262,
1.564, 1.683, 3.417, 0.65, 1.804, 2.016, 2.446, 0.702, 1.869,
0.746, 3.343, 1.033, 3.984, 1.067, 1.434, 2.076, 2.226, 4.295,
2.023, 1.016, 1.737, 3.669, 1.225, 0.485, 2.42, 3.062, 1.736,
1.372, 3.244, 2.885, 1.806, 2.403, 2.771, 1.791, 2.834, 3.889,
4.502, 2.807, 3.486, 2.375, 0.817, 1.847, 2.197, 2.185, 1.645,
1.362, 1.48, 1.149, 1.788, 2.807, 2.003, 0.997, 2.618, 1.616,
3.618, 1.369, 1.354, 0.5, 2.065, 4.543, 2.877, 1.271, 2.494,
2.778, 3.167, 1.745, 2.359, 4.095, 1.943, 1.415, 3.547, 5.202,
2.58, 1.96, 1.124, 3.238, 3.02, 1.367, 1.726, 2.302, 2.512, 0.759,
2.192, 3.15, 2.839, 4), h_7 = c(3.944, 2.971, 3.597, 7.331, 0.157,
3.246, 5.143, 4.038, 4.62, 8.276, 3.273, 4.792, 4.084, 7.116,
5.171, 4.521, 4.489, 3.858, 4.978, 4.881, 5.335, 1.361, 3.734,
2.205, 3.643, 3.594, 3.541, 2.524, 4.838, 4.157, 2.983, 6.644,
7.517, 2.41, 4.247, 5.508, 4.549, 2.551, 6.072, 6.069, 2.842,
5.862, 5.345, 3, 4.769, 2.266, 4.495, 1.15, 6.454, 4.976, 5.955,
6.088, 4.59, 2.782, 4.862, 2.28, 5.885, 2.574, 3.431, 4.878,
5.899, 5.832, 5.674, 3.591, 3.531, 4.825, 7.777, 2.232, 5.971,
6.209, 5.998, 2.159, 4.549, 2.784, 4.631, 2.271, 5.291, 3.231,
3.554, 4.512, 5.732, 8.902, 3.408, 3.22, 3.883, 6.306, 2.911,
1.414, 4.128, 3.826, 5.774, 2.821, 5.404, 5.808, 5.438, 5.799,
4.229, 4.481, 4.958, 5.625, 5.415, 4.743, 5.998, 4.464, 2.284,
3.182, 6.053, 4.695, 6.305, 3.106, 2.605, 2.989, 4.678, 4.743,
4.143, 2.808, 4.523, 4.027, 4.915, 5.688, 2.799, 1.262, 4.947,
5.731, 5.335, 3.685, 5.917, 4.241, 7.878, 3.28, 5.54, 4.96, 5.138,
4.028, 6.175, 7.239, 4.571, 4.087, 3.57, 5.434, 4.19, 3.716,
3.671, 7.065, 4.635, 1.697, 4.962, 4.667, 4.746, 4.848), h_8 = c(5.215,
5.386, 6.699, 8.865, 0.427, 5.445, 7.39, 6.853, 6.185, 7.8, 5.74,
6.424, 6.53, 7.32, 6.008, 8.395, 10.026, 4.249, 8.699, 5.004,
6.313, 2.168, 7.191, 5.241, 5.125, 5.37, 5.069, 4.746, 6.941,
7.316, 6.779, 6.306, 7.13, 4.673, 7.553, 6.066, 5.055, 4.024,
8.355, 6.071, 3.719, 6.783, 7.185, 3.995, 5.642, 4.749, 5.131,
1.833, 6.354, 6.263, 7.299, 8.336, 6.351, 4.624, 5.835, 4.439,
5.088, 4.1, 5.431, 4.44, 7.039, 6.247, 5.87, 5.735, 6.145, 6.091,
7.619, 6.102, 8.134, 6.349, 8.065, 5.498, 6.431, 4.169, 5.304,
4.546, 5.721, 5.607, 7.894, 6.478, 7.121, 7.671, 4.972, 5.923,
4.956, 7.251, 5.109, 4.452, 6.651, 4.112, 6.743, 5.306, 5.581,
6.09, 8.751, 10.775, 4.649, 6.467, 6.948, 5.593, 5.717, 5.431,
6.158, 5.759, 3.807, 3.975, 6.76, 5.866, 7.375, 4.356, 4.117,
4.146, 7.317, 5.431, 6.002, 4.177, 5.432, 6.185, 5.164, 8.952,
4.595, 3.218, 6.032, 5.805, 5.246, 4.59, 8.141, 4.648, 8.084,
6.147, 5.986, 4.995, 6.718, 4.528, 8.55, 8.742, 5.106, 6.335,
4.793, 5.607, 4.527, 9.264, 5.148, 7.653, 5.048, 3.544, 6.039,
5.443, 5.538, 4.979), h_9 = c(5.279, 5.904, 7.211, 6.111, 0.686,
5.486, 6.411, 7.185, 7.688, 5.984, 5.925, 5.703, 6.011, 6.917,
5.155, 6.805, 9.44, 4.454, 7.568, 4.831, 5.196, 1.964, 7.191,
4.502, 4.701, 4.84, 5.185, 4.929, 7.045, 7.729, 6.769, 5.887,
5.477, 5.668, 7.034, 6.077, 4.772, 4.451, 7.419, 6.329, 4.182,
6.222, 6.138, 4.144, 6.23, 4.38, 5.154, 2.3, 6.404, 5.772, 5.932,
7.208, 7.626, 4.986, 5.043, 8.145, 5.184, 4.195, 5.652, 4.941,
5.91, 5.384, 5.672, 6.187, 5.849, 6.842, 5.453, 7.599, 6.645,
4.831, 8.056, 5.92, 6.229, 4.236, 5.425, 4.728, 5.045, 5.764,
9.408, 6.174, 6.258, 6.956, 5.795, 6.728, 4.565, 6.555, 5.895,
4.633, 7.259, 4.601, 5.855, 5.48, 5.246, 5.448, 7.517, 9.931,
4.938, 6.758, 6.838, 4.945, 5.694, 5.569, 5.11, 5.72, 4.327,
4.316, 6.338, 5.586, 6.627, 4.62, 5.437, 5.406, 6.071, 5.569,
4.98, 4.102, 5.439, 7.023, 5.06, 6.871, 5.272, 3.925, 6.269,
5.077, 4.981, 4.224, 6.76, 4.936, 7.325, 6.029, 5.669, 5.122,
6.133, 4.009, 8.74, 8.375, 4.909, 5.907, 4.212, 5.546, 4.625,
9.848, 5.362, 6.648, 4.422, 3.788, 6.14, 5.741, 5.806, 5.027),
h_10 = c(5.058, 6.346, 6.55, 5.07, 1.484, 5.323, 5.278, 5.735,
6.742, 5.904, 5.429, 5.483, 5.835, 6.039, 4.841, 5.971, 6.849,
5.019, 5.946, 5.286, 4.46, 2.251, 5.69, 4.145, 4.659, 4.651,
4.937, 4.407, 6.683, 8.145, 6.157, 5.74, 5.485, 6.393, 7.573,
6.145, 4.81, 4.735, 5.986, 6.048, 4.754, 6.089, 5.299, 4.212,
5.896, 4.195, 5.432, 4.06, 5.801, 4.853, 5.505, 6.439, 8.785,
5.16, 4.865, 5.701, 6.12, 4.608, 5.585, 5.691, 5.775, 5.481,
5.769, 5.989, 5.114, 6.312, 4.829, 5.96, 5.713, 4.073, 6.565,
4.873, 5.742, 5.089, 5.368, 4.296, 4.905, 5.46, 6.302, 6.095,
5.621, 6.09, 5.853, 6.594, 4.785, 5.915, 6.814, 4.733, 7.454,
4.967, 6.562, 5.022, 5.416, 5.736, 6.562, 7.703, 5.361, 7.068,
5.823, 5.008, 5.717, 6.034, 5.176, 5.567, 4.828, 4.853, 5.759,
5.522, 6.224, 5.135, 6.105, 6.028, 5.328, 6.034, 5.202, 4.424,
5.67, 5.98, 5.371, 5.011, 5.106, 4.307, 6.163, 5.434, 5.086,
4.31, 5.25, 5.36, 5.911, 5.119, 5.45, 5.3, 5.851, 4.142,
5.795, 5.223, 5.202, 4.818, 4.274, 5.377, 5.083, 7.644, 5.714,
5.638, 4.582, 4.417, 6.002, 5.24, 6.413, 5.264), h_11 = c(5.189,
7.161, 6.16, 5.029, 3.229, 5.663, 5.523, 6.22, 5.834, 5.981,
5.588, 5.924, 6.1, 5.593, 5.359, 5.823, 5.877, 5.658, 6.034,
5.53, 4.847, 3.975, 5.727, 4.918, 5.083, 5.428, 5.219, 4.19,
6.593, 8.498, 5.693, 5.474, 5.866, 7.03, 7.822, 6.103, 4.899,
5.251, 5.579, 5.878, 5.56, 6.383, 5.226, 4.756, 6.012, 4.302,
5.936, 3.881, 5.65, 4.818, 5.626, 6.501, 4.288, 5.74, 5.171,
6.108, 6.609, 5.514, 5.815, 7.067, 5.748, 5.871, 6.02, 6.103,
5.188, 6.302, 4.994, 6.102, 5.514, 4.232, 4.934, 4.352, 5.851,
6.021, 5.562, 3.678, 5.036, 5.673, 4.629, 6.192, 5.913, 5.603,
5.916, 7.591, 5.181, 5.692, 7.577, 5.298, 7.374, 5.33, 6.885,
5.202, 5.675, 6.281, 6.411, 5.672, 5.839, 7.519, 6.107, 5.004,
6.014, 6.47, 5.543, 5.677, 5.682, 5.023, 6.043, 5.651, 6.42,
5.696, 6.552, 6.117, 5.337, 6.47, 5.716, 5.585, 6.013, 5.962,
5.692, 4.826, 6.334, 6.454, 6.221, 5.687, 5.396, 5.452, 5.035,
5.838, 5.372, 4.676, 5.881, 5.53, 5.994, 5.085, 4.497, 4.996,
5.709, 4.862, 5.015, 5.277, 5.425, 6.354, 6.517, 5.427, 5.353,
5.554, 5.542, 5.476, 7.077, 5.483), h_12 = c(6.006, 7.094,
5.992, 4.892, 5.527, 5.758, 5.853, 6.067, 5.441, 5.388, 5.872,
6.497, 6.347, 5.749, 5.449, 5.799, 5.769, 5.261, 6.084, 5.822,
4.877, 2.203, 6.523, 6.14, 5.972, 5.421, 5.607, 4.782, 6.095,
8.027, 5.084, 5.227, 5.285, 7.219, 8.326, 5.96, 4.82, 5.55,
5.881, 5.624, 6.303, 6.584, 5.299, 5.366, 7.179, 4.949, 5.607,
5.102, 5.977, 5.271, 5.926, 6.274, 5.239, 6.359, 5.375, 6.231,
6.533, 6.817, 5.978, 6.754, 5.845, 6.12, 5.96, 6.148, 5.58,
6.066, 5.093, 6.271, 5.443, 5.151, 5.033, 5.141, 6.123, 6.887,
5.763, 4.457, 4.872, 5.669, 4.608, 6.125, 6.323, 5.127, 6.01,
5.655, 5.62, 6.021, 7.806, 5.97, 6.284, 5.317, 6.945, 5.344,
5.857, 5.594, 6.486, 5.019, 5.764, 7.185, 6.517, 4.913, 5.67,
6.085, 5.197, 5.733, 6.351, 4.874, 5.961, 5.461, 6.546, 6.145,
7.203, 6.776, 5.585, 6.085, 5.576, 6.505, 6.235, 6.488, 5.459,
5.14, 5.987, 6.034, 6.521, 6.028, 5.297, 6.444, 5.302, 5.763,
5.304, 5.01, 6.146, 5.496, 6.166, 5.821, 5.193, 5.692, 5.393,
5.274, 5.633, 5.832, 5.267, 6.054, 6.359, 5.537, 5.942, 5.417,
5.874, 5.397, 6.357, 5.321), h_13 = c(6.382, 7.456, 5.787,
5.111, 8.092, 5.445, 5.874, 6.724, 5.643, 5.912, 5.375, 5.762,
6.451, 5.818, 5.291, 5.136, 5.244, 5.707, 5.607, 6.193, 4.612,
3.928, 6.428, 8.983, 6.057, 6.555, 6.157, 5.853, 6.179, 5.981,
4.841, 5.41, 5.753, 7, 8.053, 5.501, 4.74, 4.947, 6.016,
5.256, 6.574, 6.457, 4.814, 6.047, 7.346, 5.871, 5.659, 7.654,
5.198, 5.101, 5.81, 5.447, 4.822, 6.117, 4.999, 6.068, 6.337,
6.293, 5.421, 6.567, 5.83, 6.171, 5.885, 6.25, 6.075, 6.12,
4.863, 5.763, 5.438, 5.849, 5.203, 6.08, 6.343, 6.008, 6.01,
5.84, 4.99, 5.15, 4.9, 5.82, 5.972, 4.861, 5.949, 4.792,
5.057, 6.005, 7.517, 6.63, 5.745, 5.071, 6.42, 5.11, 5.905,
6.089, 6.229, 4.908, 5.724, 6.269, 6.566, 5.418, 5.983, 6.295,
5.578, 5.634, 6.518, 4.916, 5.878, 5.115, 6.017, 5.491, 6.706,
6.965, 5.24, 6.295, 5.458, 6.077, 6.325, 6.684, 5.684, 5.056,
5.306, 6.174, 6.427, 5.738, 4.824, 6.271, 5.476, 5.723, 4.761,
5.836, 5.52, 5.633, 5.515, 5.849, 4.908, 5.357, 5.863, 5.775,
5.497, 6.402, 5.548, 5.791, 5.729, 5.537, 5.428, 5.091, 6.287,
4.913, 6.385, 5.436), h_14 = c(6.865, 5.34, 5.906, 6.166,
9.527, 6.315, 6.553, 6.379, 6.105, 6.025, 6.292, 6.424, 6.883,
6.203, 5.484, 6.954, 6.694, 6.35, 6.6, 6.346, 4.679, 6.227,
6.058, 6.076, 5.972, 6.76, 6.654, 6.336, 5.184, 5.248, 5.422,
5.054, 5.889, 4.89, 5.566, 6.149, 5.025, 5.514, 7.41, 4.755,
6.912, 6.719, 5.293, 6.723, 6.496, 6.209, 5.786, 8.121, 5.55,
5.609, 6.491, 4.488, 5.447, 6.319, 6.112, 6.516, 6.502, 5.911,
6.069, 6.692, 7.081, 6.498, 5.976, 6.348, 6.311, 6.341, 5.381,
7.006, 5.965, 5.37, 5.652, 6.401, 6.82, 6.394, 6.207, 6.547,
5.016, 6.152, 5.456, 5.946, 6.595, 4.944, 6.151, 6.095, 5.714,
5.279, 5.83, 6.864, 5.711, 5.508, 7.248, 5.787, 6.396, 6.47,
4.872, 5.098, 6.271, 5.829, 6.88, 5.547, 5.769, 6.688, 5.786,
6.033, 6.425, 5.2, 6.2, 5.459, 6.834, 5.91, 5.718, 6.784,
6.603, 6.688, 5.405, 6.225, 6.74, 7.376, 5.74, 6.335, 5.935,
6.486, 6.772, 5.953, 5.135, 8.082, 5.81, 6.27, 5.372, 6.161,
5.642, 6.044, 6.19, 6.189, 5.193, 5.573, 6.394, 6.608, 5.954,
6.519, 5.845, 6.174, 5.795, 6.169, 5.288, 5.769, 6.364, 5.253,
6.865, 5.5), h_15 = c(7.454, 5.195, 5.94, 6.002, 10.864,
6.654, 6.799, 6.13, 5.498, 6.077, 6.352, 6.776, 6.88, 6.709,
5.871, 6.426, 6.077, 6.678, 6.65, 6.6, 4.99, 8.095, 5.381,
5.34, 5.845, 6.582, 7.072, 6.841, 5.417, 6.091, 7.357, 4.885,
6.02, 5.261, 4.931, 6.01, 5.036, 5.988, 8.589, 5.737, 7.698,
6.582, 5.255, 7.67, 5.562, 6.825, 5.761, 11.858, 5.826, 6.003,
6.589, 6.054, 6.282, 6.523, 6.136, 8.43, 6.082, 6.404, 6.26,
7.192, 6.736, 6.455, 6.068, 6.549, 6.964, 6.164, 5.568, 6.864,
6.019, 5.55, 5.904, 6.778, 7.021, 6.847, 6.406, 7.216, 5.114,
6.28, 5.775, 5.734, 6.615, 6.213, 6.276, 7.322, 6.023, 5.611,
5.306, 6.76, 5.528, 5.739, 7.329, 6.309, 7.257, 6.663, 5.473,
5.547, 6.534, 5.841, 6.962, 5.748, 5.743, 6.83, 5.843, 5.92,
6.964, 5.049, 6.489, 5.705, 6.73, 6.203, 5.531, 7.219, 6.125,
6.83, 5.7, 6.524, 7.36, 8.519, 5.953, 5.96, 6.946, 7.938,
6.982, 6.174, 5.345, 7.418, 6.511, 6.533, 5.5, 6.58, 6.061,
6.319, 6.395, 6.557, 5.7, 6.636, 6.572, 7.005, 6.473, 6.506,
6.007, 5.993, 6.241, 6.091, 5.691, 6.779, 6.31, 6.182, 7.12,
5.51), h_16 = c(7.353, 5.787, 6.161, 6.509, 11.262, 6.6,
6.672, 6.25, 5.535, 6.324, 6.301, 6.674, 6.839, 6.908, 6.514,
6.121, 5.723, 7.035, 6.788, 6.444, 5.472, 10.921, 5.469,
6.733, 6.099, 7.474, 7.784, 8.487, 6.129, 6.309, 8.839, 4.975,
6.244, 6.157, 5.251, 5.895, 5.091, 6.433, 7.946, 6.376, 8.058,
6.393, 5.201, 8.733, 5.122, 8.096, 5.822, 14.05, 6.429, 7.071,
6.739, 6.508, 9.411, 6.858, 6.112, 7.9, 5.593, 6.642, 6.337,
9.631, 6.39, 6.58, 6.185, 6.99, 7.174, 6.788, 6.501, 6.554,
6.3, 6.069, 6.71, 8.661, 7.087, 7.406, 6.401, 8.674, 5.231,
6.311, 6.501, 5.362, 6.612, 6.229, 6.31, 7.476, 6.371, 5.721,
5.987, 7.538, 5.516, 5.92, 6.986, 7.295, 7.904, 6.874, 5.512,
5.875, 6.642, 6.295, 7.16, 5.927, 5.687, 6.876, 5.897, 5.846,
6.982, 5.035, 6.525, 6.14, 6.65, 6.413, 5.853, 6.836, 6.103,
6.876, 7.094, 6.733, 7.558, 8.504, 6.279, 5.826, 7.607, 9.105,
6.933, 6.308, 5.709, 8.642, 7.368, 6.641, 5.486, 7.448, 6.471,
6.54, 6.284, 7.538, 5.985, 7.316, 6.634, 7.738, 7.202, 6.59,
6.25, 6.21, 7.009, 6.275, 6.944, 8.511, 6.414, 6.345, 8.462,
5.458), h_17 = c(7.167, 7.165, 5.919, 7.756, 12.506, 7.129,
7.412, 6.438, 5.298, 6.466, 6.854, 7.129, 7.202, 6.979, 6.77,
6.627, 6.324, 7.777, 7.203, 6.508, 5.667, 8.669, 6.065, 9.439,
7.285, 7.226, 8.281, 8.832, 6.582, 6.924, 8.522, 5.317, 6.729,
7.497, 6.009, 5.773, 5.262, 7.128, 7.873, 6.709, 8.085, 6.174,
5.836, 9.419, 4.893, 9.529, 5.867, 11.822, 6.705, 7.529,
8.222, 6.754, 9.434, 7.511, 6.234, 9.366, 5.612, 7.929, 6.565,
11.007, 6.612, 6.502, 5.569, 7.629, 7.499, 6.537, 8.403,
7.203, 7.194, 9.064, 7.337, 9.488, 7.423, 9.125, 6.571, 9.008,
5.25, 6.816, 7.807, 4.967, 7.059, 6.581, 6.776, 6.44, 7.372,
6.307, 7.067, 7.937, 6.697, 6.099, 6.541, 7.105, 7.735, 7.206,
6.397, 6.699, 6.785, 7.179, 6.538, 5.999, 5.715, 7.28, 5.899,
6.314, 7.874, 4.973, 6.749, 6.529, 7.329, 6.864, 6.686, 6.716,
6.861, 7.28, 7.058, 7.46, 7.692, 8.819, 6.566, 6.706, 7.498,
8.927, 7.233, 6.051, 5.679, 9.051, 8.124, 6.784, 6.083, 8.368,
6.798, 6.812, 6.552, 9.764, 6.555, 7.427, 6.784, 8.472, 9.907,
6.597, 6.547, 6.019, 7.633, 6.337, 7.115, 8.625, 6.184, 6.103,
8.772, 5.442), h_18 = c(7.058, 7.77, 5.969, 8.633, 12.037,
7.306, 6.894, 6.405, 5.153, 6.146, 7.364, 7.364, 6.957, 5.973,
7.169, 6.985, 6.725, 7.839, 6.587, 6.543, 5.967, 11.16, 6.889,
9.07, 8.09, 6.462, 7.865, 8.502, 7.144, 7.165, 8.531, 5.366,
6.528, 7.46, 6.469, 5.544, 5.238, 6.939, 6.006, 6.491, 7.755,
6.095, 5.895, 9.065, 4.411, 9.792, 5.774, 9.019, 6.529, 7.222,
7.882, 7.166, 10.153, 7.306, 6.164, 7.33, 5.754, 9.185, 6.489,
7.255, 5.806, 5.824, 6.048, 7.509, 7.557, 6.832, 9.135, 7.684,
7.419, 11.18, 7.139, 9.235, 7.238, 9.511, 6.481, 8.704, 5.364,
6.689, 8.963, 4.646, 6.716, 6.597, 6.789, 7.246, 7.212, 6.937,
7.719, 8.534, 9.163, 6.1, 5.794, 7.592, 7.438, 7.023, 6.806,
7.155, 6.878, 8.076, 6.093, 5.725, 5.875, 7.098, 5.715, 6.532,
8.449, 4.723, 6.721, 6.45, 6.776, 6.859, 7.236, 6.727, 7.348,
7.098, 7.021, 7.778, 6.834, 7.109, 6.399, 7.01, 7.898, 8.565,
6.871, 5.729, 5.585, 7.22, 8.55, 6.877, 6.558, 8.775, 6.949,
6.736, 6.673, 9.698, 7.03, 7.066, 6.649, 7.933, 9.846, 6.694,
6.554, 6.14, 7.51, 6.06, 6.983, 8.531, 5.996, 5.576, 7.289,
5.478), h_19 = c(5.687, 8.075, 5.892, 6.372, 10.094, 6.505,
6.055, 5.797, 4.308, 4.77, 6.675, 6.218, 5.605, 4.336, 6.558,
5.887, 5.707, 6.176, 5.783, 6.067, 5.872, 11.352, 6.618,
7.651, 7.454, 5.176, 6.72, 7.979, 6.034, 5.747, 8.054, 4.695,
4.984, 7.736, 6.157, 5.458, 5.261, 6.257, 3.821, 6.21, 6.625,
4.79, 5.316, 7.361, 4.711, 9.315, 5.403, 5.857, 5.525, 5.933,
6.151, 6.781, 4.937, 7.457, 5.419, 7.371, 5.079, 8.358, 6.193,
4.878, 5.904, 4.811, 6.298, 6.727, 7.392, 6.331, 6.913, 6.525,
6.486, 8.624, 6.014, 7.782, 5.672, 7.646, 5.664, 8.11, 5.042,
6.073, 8.246, 5.056, 5.858, 5.91, 5.882, 6.555, 6.22, 6.095,
7.354, 8.002, 4.622, 6.014, 5.29, 8.174, 5.627, 5.462, 6.43,
6.281, 6.237, 7.622, 4.942, 5.132, 5.341, 5.682, 5.091, 6.343,
8.041, 4.818, 6.213, 5.921, 5.557, 6.2, 7.53, 6.659, 6.437,
5.682, 6.235, 7.109, 5.464, 4.284, 5.601, 6.94, 8.228, 9.3,
5.611, 5.032, 5.403, 7.09, 6.221, 6.236, 5.1, 8.594, 6.678,
6.037, 5.728, 7.849, 5.225, 4.217, 5.536, 6.219, 7.906, 6.242,
5.73, 5.873, 6.65, 5.933, 6.499, 8.912, 6.167, 5.503, 4.775,
5.145), h_20 = c(4.335, 7.319, 5.038, 3.809, 7.279, 5.174,
4.37, 4.575, 4.01, 2.962, 4.964, 4.469, 4.154, 2.597, 5.11,
4.389, 4.196, 4.113, 4.463, 4.879, 4.825, 6.801, 4.192, 6.711,
5.633, 3.724, 4.825, 5.548, 5.191, 3.998, 4.551, 3.612, 3.448,
7.235, 5.353, 4.955, 4.804, 5.121, 2.528, 5.686, 4.958, 3.28,
4.306, 4.993, 4.507, 6.502, 4.176, 4.384, 4.169, 5.125, 4.224,
5.82, 2.643, 5.897, 4.583, 3.95, 4.013, 5.609, 5.064, 3.315,
4.745, 3.624, 4.79, 4.735, 5.903, 5.266, 4.293, 4.887, 4.835,
4.672, 4.213, 4.997, 3.919, 5.129, 4.28, 5.412, 4.299, 4.906,
5.149, 4.539, 4.291, 5.092, 4.387, 4.581, 4.551, 5.163, 6.564,
6.223, 3.045, 5.073, 3.796, 5.932, 3.251, 3.328, 5.627, 4.159,
4.307, 5.604, 3.305, 4.146, 3.588, 3.425, 4.128, 5.207, 5.942,
5.47, 4.795, 4.636, 3.923, 5.068, 7.024, 5.559, 4.797, 3.425,
4.749, 5.418, 3.967, 2.817, 4.05, 4.93, 6.056, 5.937, 3.952,
4.567, 4.945, 4.655, 3.797, 4.306, 3.789, 5.892, 5.141, 4.769,
4.452, 4.943, 3.388, 2.495, 3.919, 4.386, 5.201, 4.942, 4.51,
4.579, 4.658, 5.084, 5.059, 6.827, 5.386, 4.819, 3.15, 4.386
), h_21 = c(3.86, 3.419, 4.111, 2.631, 2.901, 3.924, 3.444,
3.567, 3.663, 2.51, 3.592, 3.19, 3.056, 1.699, 3.313, 3.106,
2.53, 4.047, 2.854, 3.757, 3.214, 5.125, 3.464, 3.532, 4.447,
2.206, 3.573, 4.029, 3.56, 2.206, 3.041, 3.331, 3.154, 3.713,
2.721, 3.886, 3.941, 4.302, 1.914, 3.58, 3.578, 2.488, 3.295,
3.419, 3.464, 4.121, 3.959, 2.623, 3.114, 3.845, 2.729, 3.271,
2.364, 4.42, 3.901, 2.958, 3.419, 3.846, 3.942, 2.502, 3.382,
2.949, 2.888, 3.22, 3.898, 3.666, 2.721, 3.333, 3.232, 3.074,
2.769, 3.477, 2.933, 3.637, 3.498, 3.93, 4.048, 4.086, 2.949,
3.302, 3.14, 2.861, 3.726, 3.719, 3.748, 3.726, 2.921, 4.167,
2.42, 3.438, 2.806, 4.92, 2.626, 3.024, 3.408, 2.507, 3.624,
2.182, 2.355, 4.125, 2.99, 2.472, 4.123, 4.021, 3.955, 4.36,
3.393, 3.194, 2.623, 4.183, 4.177, 4.048, 3.315, 2.472, 3.006,
4.156, 2.923, 2.275, 3.577, 3.417, 4.577, 4.397, 2.805, 3.977,
3.541, 3.47, 2.691, 3.623, 3.066, 3.351, 2.95, 3.814, 3.464,
3.415, 2.565, 1.514, 4.005, 3.375, 3.57, 3.788, 4.596, 2.815,
2.734, 3.424, 3.232, 5.065, 4.094, 4.471, 2.373, 4.404),
h_22 = c(3.696, 2.023, 3.479, 2.055, 2.163, 3.123, 2.472,
2.54, 3.189, 2.453, 2.989, 2.69, 2.246, 1.216, 3.239, 2.623,
1.928, 4.207, 2.124, 2.968, 3.213, 3.784, 2.654, 2.123, 3.304,
2.814, 2.691, 3.423, 2.341, 1.337, 2.192, 3.08, 3.232, 2.579,
1.511, 3.344, 4.409, 4.034, 1.686, 2.237, 2.774, 2.157, 2.773,
2.464, 3.446, 2.751, 3.929, 2.048, 2.612, 3.692, 2.106, 1.589,
2.063, 3.477, 3.512, 2.851, 3.059, 3.226, 3.348, 2.064, 3.048,
2.397, 2.743, 2.451, 2.823, 2.567, 2.173, 2.458, 2.375, 2.476,
2.321, 2.831, 2.438, 2.611, 3.325, 3.481, 4.156, 3.557, 2.092,
4.33, 2.636, 1.537, 3.45, 2.511, 3.678, 2.096, 1.851, 3.461,
2.603, 3.488, 2.362, 3.282, 2.314, 3.142, 1.986, 1.642, 3.632,
1.055, 2.153, 4.491, 2.856, 2.397, 4.122, 3.356, 2.934, 4.786,
2.589, 3.187, 2.048, 4.002, 2.735, 2.987, 2.698, 2.397, 2.828,
3.752, 2.097, 2.043, 3.777, 2.9, 2.703, 2.717, 2.257, 3.32,
3.618, 2.996, 2.167, 3.632, 2.673, 2.361, 2.528, 3.243, 2.883,
2.632, 1.963, 1.051, 4.194, 2.675, 2.631, 2.803, 4.846, 2.025,
2.77, 2.626, 2.987, 3.567, 3.198, 3.879, 1.992, 4.539), h_23 = c(2.771,
1.806, 3.231, 1.822, 0.874, 3.096, 1.884, 2.118, 3.401, 1.712,
2.575, 2.425, 1.7, 0.833, 3.21, 2.331, 1.635, 3.212, 1.81,
2.477, 2.83, 3.832, 2.955, 2.364, 3.092, 3.731, 2.257, 2.996,
2.081, 1.062, 1.65, 2.328, 2.478, 2.521, 1.246, 3.046, 4.689,
3.862, 1.118, 1.894, 2.37, 1.515, 2.688, 2.22, 3.068, 2.166,
3.274, 1.653, 2.135, 2.91, 1.881, 1.311, 1.53, 2.917, 3.262,
1.914, 2.184, 3.067, 2.963, 1.126, 2.437, 1.724, 2.374, 2.059,
2.302, 1.865, 1.824, 2.203, 1.893, 2.236, 2.286, 2.196, 1.89,
2.371, 2.525, 3.207, 3.87, 3.359, 1.699, 4.334, 1.992, 1.304,
3.103, 2.454, 3.464, 1.819, 1.758, 3.134, 2.076, 3.827, 1.898,
3.213, 1.611, 2.344, 1.466, 1.318, 2.943, 0.808, 1.592, 3.638,
2.408, 1.957, 3.311, 2.834, 2.711, 5.069, 1.998, 3.226, 1.703,
3.527, 2.505, 2.487, 2.322, 1.957, 3.006, 3.355, 1.529, 1.497,
2.97, 2.723, 2.029, 2.036, 1.741, 2.5, 4.043, 2.586, 1.534,
2.942, 2.556, 1.832, 2.586, 2.321, 2.488, 2.472, 2.027, 0.891,
3.262, 2.081, 2.582, 2.053, 3.648, 1.831, 2.555, 2.312, 3.148,
2.915, 2.893, 3.55, 0.353, 3.713), h_24 = c(1.516, 1.248,
1.984, 0.918, 0.314, 2.254, 1.036, 1.374, 1.011, 1, 1.993,
1.617, 1.244, 0.555, 2.287, 1.777, 1.033, 1.891, 1.031, 1.717,
2.167, 2.443, 1.655, 1.944, 2.202, 3.513, 1.457, 1.779, 1.281,
0.745, 0.987, 1.579, 1.433, 1.748, 0.825, 2.249, 4.116, 3.06,
0.679, 1.393, 1.779, 0.978, 2.229, 1.602, 1.854, 1.215, 2.428,
0.503, 1.557, 1.299, 1.148, 0.801, 0.487, 1.878, 2.732, 0.652,
1.45, 2.161, 2.309, 0.313, 1.683, 1.293, 1.692, 1.547, 1.174,
1.252, 1.102, 1.525, 1.292, 1.338, 1.234, 1.309, 1.27, 1.452,
1.584, 1.97, 3.122, 2.457, 1.055, 2.882, 1.158, 0.83, 2.086,
1.878, 2.694, 1.223, 1.133, 1.786, 1.089, 3.285, 1.131, 2.242,
1.025, 1.362, 0.956, 0.597, 2.006, 0.465, 1.102, 2.474, 1.779,
1.363, 2.129, 2.214, 1.95, 4.824, 1.127, 2.634, 1.07, 2.754,
1.954, 1.576, 1.76, 1.363, 2.411, 2.436, 1.027, 0.843, 1.989,
2.183, 1.383, 1.187, 1.211, 1.204, 3.67, 1.271, 0.774, 2.006,
1.825, 1.212, 1.921, 1.468, 1.728, 1.623, 1.678, 0.444, 2.039,
1.32, 1.767, 1.336, 2.22, 1.008, 1.943, 1.45, 2.728, 2.065,
1.78, 2.981, 0.24, 2.61)), class = "data.frame", row.names = c(NA,
-150L))


There are different ways of achieving this. In general, you are looking for some unsupervised learning method (have some unlabelled data with characteristics and want to group observations (roads) based on similarity)
First note that in your data, type includes duplicates. That should not be the case, if each row is a different street. I assume this is a mistake:
d$type <- paste0("id_", 1:nrow(d))
dd <- as.matrix(d[,-1])
rownames(dd) <- d$type
K-means clustering:
dd <- scale(dd)
# 4 means clusering
set.seed(123)
km.res <- kmeans(dd, 15, nstart = 25)
# get cluster membership
km.res$cluster[1:10]
id_1 id_2 id_3 id_4 id_5 id_6 id_7 id_8 id_9 id_10
3 10 3 6 2 9 3 3 12 15
Alternatively, hierarchical clustering:
# hierarchical clustering
dist_mat <- dist(dd, method = 'euclidean')
hclust_avg <- hclust(dist_mat, method = 'average')
plot(hclust_avg)
cut_avg <- cutree(hclust_avg, k = 15)
plot(hclust_avg)
rect.hclust(hclust_avg , k = 15, border = 2:6)
abline(h = 3, col = 'red')
# get cluster membership:
cut_avg[1:10]
id_1 id_2 id_3 id_4 id_5 id_6 id_7 id_8 id_9 id_10
1 2 3 3 4 3 3 3 5 3
Note that in general different methods will have different results. If you look into the help files of the functions you will find more information about the possible options for each method, eg for the definition of distance, and for how to compute the clusters (average, max, min, ward).

Related

Change proportion of zoom in facet_zoom [ggplot2]

I would like to change the proportion of the graph covered by the "zoom". If we look at the following image we are at a ratio "graph:zoom" around 1:2 I would like instead a ratio 2:1. In other words, what I want is to reduce the height of the zoom. How should I proceed?
Here is my code
require(dplyr)
require(tidyverse)
require(ggforce)
HY <- DebitH %>%
ggplot(aes(x = Date, y = Débit_horaire)) +
geom_point(alpha = 6/10, size = 0.3, color = "blue") +
geom_line(alpha = 4/10, size = 0.5, color = "blue") +
labs(x = "Date", y = "Débit Horaire (m3/s)")+
theme_bw() +
theme(panel.grid.major.y = element_line(color = "grey",
size = 0.25,
linetype = 2),
legend.position = "none") +
facet_zoom(xlim = as.POSIXct(c("2021-01-15 00:00:00","2021-02-15 00:00:00")))
And here you will find a sample of the data
DebitH <-
structure(list(Date = structure(c(1610233200, 1610236800, 1610240400,
1610244000, 1610247600, 1610251200, 1610254800, 1610258400, 1610262000,
1610265600, 1610269200, 1610272800, 1610276400, 1610280000, 1610283600,
1610287200, 1610290800, 1610294400, 1610298000, 1610301600, 1610305200,
1610308800, 1610312400, 1610316000, 1610319600, 1610323200, 1610326800,
1610330400, 1610334000, 1610337600, 1610341200, 1610344800, 1610348400,
1610352000, 1610355600, 1610359200, 1610362800, 1610366400, 1610370000,
1610373600, 1610377200, 1610380800, 1610384400, 1610388000, 1610391600,
1610395200, 1610398800, 1610402400, 1610406000, 1610409600, 1610413200,
1610416800, 1610420400, 1610424000, 1610427600, 1610431200, 1610434800,
1610438400, 1610442000, 1610445600, 1610449200, 1610452800, 1610456400,
1610460000, 1610463600, 1610467200, 1610470800, 1610474400, 1610478000,
1610481600, 1610485200, 1610488800, 1610492400, 1610496000, 1610499600,
1610503200, 1610506800, 1610510400, 1610514000, 1610517600, 1610521200,
1610524800, 1610528400, 1610532000, 1610535600, 1610539200, 1610542800,
1610546400, 1610550000, 1610553600, 1610557200, 1610560800, 1610564400,
1610568000, 1610571600, 1610575200, 1610578800, 1610582400, 1610586000,
1610589600, 1610593200, 1610596800, 1610600400, 1610604000, 1610607600,
1610611200, 1610614800, 1610618400, 1610622000, 1610625600, 1610629200,
1610632800, 1610636400, 1610640000, 1610643600, 1610647200, 1610650800,
1610654400, 1610658000, 1610661600, 1610665200, 1610668800, 1610672400,
1610676000, 1610679600, 1610683200, 1610686800, 1610690400, 1610694000,
1610697600, 1610701200, 1610704800, 1610708400, 1610712000, 1610715600,
1610719200, 1610722800, 1610726400, 1610730000, 1610733600, 1610737200,
1610740800, 1610744400, 1610748000, 1610751600, 1610755200, 1610758800,
1610762400, 1610766000, 1610769600, 1610773200, 1610776800, 1610780400,
1610784000, 1610787600, 1610791200, 1610794800, 1610798400, 1610802000,
1610805600, 1610809200, 1610812800, 1610816400, 1610820000, 1610823600,
1610827200, 1610830800, 1610834400, 1610838000, 1610841600, 1610845200,
1610848800, 1610852400, 1610856000, 1610859600, 1610863200, 1610866800,
1610870400, 1610874000, 1610877600, 1610881200, 1610884800, 1610888400,
1610892000, 1610895600, 1610899200, 1610902800, 1610906400, 1610910000,
1610913600, 1610917200, 1610920800, 1610924400, 1610928000, 1610931600,
1610935200, 1610938800, 1610942400, 1610946000, 1610949600, 1610953200,
1610956800, 1610960400, 1610964000, 1610967600, 1610971200, 1610974800,
1610978400, 1610982000, 1610985600, 1610989200, 1610992800, 1610996400,
1.611e+09, 1611003600, 1611007200, 1611010800, 1611014400, 1611018000,
1611021600, 1611025200, 1611028800, 1611032400, 1611036000, 1611039600,
1611043200, 1611046800, 1611050400, 1611054000, 1611057600, 1611061200,
1611064800, 1611068400, 1611072000, 1611075600, 1611079200, 1611082800,
1611086400, 1611090000, 1611093600, 1611097200, 1611100800, 1611104400,
1611108000, 1611111600, 1611115200, 1611118800, 1611122400, 1611126000,
1611129600, 1611133200, 1611136800, 1611140400, 1611144000, 1611147600,
1611151200, 1611154800, 1611158400, 1611162000, 1611165600, 1611169200,
1611172800, 1611176400, 1611180000, 1611183600, 1611187200, 1611190800,
1611194400, 1611198000, 1611201600, 1611205200, 1611208800, 1611212400,
1611216000, 1611219600, 1611223200, 1611226800, 1611230400, 1611234000,
1611237600, 1611241200, 1611244800, 1611248400, 1611252000, 1611255600,
1611259200, 1611262800, 1611266400, 1611270000, 1611273600, 1611277200,
1611280800, 1611284400, 1611288000, 1611291600, 1611295200, 1611298800,
1611302400, 1611306000, 1611309600, 1611313200, 1611316800, 1611320400,
1611324000, 1611327600, 1611331200, 1611334800, 1611338400, 1611342000,
1611345600, 1611349200, 1611352800, 1611356400, 1611360000, 1611363600,
1611367200, 1611370800, 1611374400, 1611378000, 1611381600, 1611385200,
1611388800, 1611392400, 1611396000, 1611399600, 1611403200, 1611406800,
1611410400, 1611414000, 1611417600, 1611421200, 1611424800, 1611428400,
1611432000, 1611435600, 1611439200, 1611442800, 1611446400, 1611450000,
1611453600, 1611457200, 1611460800, 1611464400, 1611468000, 1611471600,
1611475200, 1611478800, 1611482400, 1611486000, 1611489600, 1611493200,
1611496800, 1611500400, 1611504000, 1611507600, 1611511200, 1611514800,
1611518400, 1611522000, 1611525600, 1611529200, 1611532800, 1611536400,
1611540000, 1611543600, 1611547200, 1611550800, 1611554400, 1611558000,
1611561600, 1611565200, 1611568800, 1611572400, 1611576000, 1611579600,
1611583200, 1611586800, 1611590400, 1611594000, 1611597600, 1611601200,
1611604800, 1611608400, 1611612000, 1611615600, 1611619200, 1611622800,
1611626400, 1611630000, 1611633600, 1611637200, 1611640800, 1611644400,
1611648000, 1611651600, 1611655200, 1611658800, 1611662400, 1611666000,
1611669600, 1611673200, 1611676800, 1611680400, 1611684000, 1611687600,
1611691200, 1611694800, 1611698400, 1611702000, 1611705600, 1611709200,
1611712800, 1611716400, 1611720000, 1611723600, 1611727200, 1611730800,
1611734400, 1611738000, 1611741600, 1611745200, 1611748800, 1611752400,
1611756000, 1611759600, 1611763200, 1611766800, 1611770400, 1611774000,
1611777600, 1611781200, 1611784800, 1611788400, 1611792000, 1611795600,
1611799200, 1611802800, 1611806400, 1611810000, 1611813600, 1611817200,
1611820800, 1611824400, 1611828000, 1611831600, 1611835200, 1611838800,
1611842400, 1611846000, 1611849600, 1611853200, 1611856800, 1611860400,
1611864000, 1611867600, 1611871200, 1611874800, 1611878400, 1611882000,
1611885600, 1611889200, 1611892800, 1611896400, 1611900000, 1611903600,
1611907200, 1611910800, 1611914400, 1611918000, 1611921600, 1611925200,
1611928800, 1611932400, 1611936000, 1611939600, 1611943200, 1611946800,
1611950400, 1611954000, 1611957600, 1611961200, 1611964800, 1611968400,
1611972000, 1611975600, 1611979200, 1611982800, 1611986400, 1611990000,
1611993600, 1611997200, 1612000800, 1612004400, 1612008000, 1612011600,
1612015200, 1612018800, 1612022400, 1612026000, 1612029600, 1612033200,
1612036800, 1612040400, 1612044000, 1612047600, 1612051200, 1612054800,
1612058400, 1612062000, 1612065600, 1612069200, 1612072800, 1612076400,
1612080000, 1612083600, 1612087200, 1612090800, 1612094400, 1612098000,
1612101600, 1612105200, 1612108800, 1612112400, 1612116000, 1612119600,
1612123200, 1612126800, 1612130400, 1612134000, 1612137600, 1612141200,
1612144800, 1612148400, 1612152000, 1612155600, 1612159200, 1612162800,
1612166400, 1612170000, 1612173600, 1612177200, 1612180800, 1612184400,
1612188000, 1612191600, 1612195200, 1612198800, 1612202400, 1612206000,
1612209600, 1612213200, 1612216800, 1612220400, 1612224000, 1612227600,
1612231200, 1612234800, 1612238400, 1612242000, 1612245600, 1612249200,
1612252800, 1612256400, 1612260000, 1612263600, 1612267200, 1612270800,
1612274400, 1612278000, 1612281600, 1612285200, 1612288800, 1612292400,
1612296000, 1612299600, 1612303200, 1612306800, 1612310400, 1612314000,
1612317600, 1612321200, 1612324800, 1612328400, 1612332000, 1612335600,
1612339200, 1612342800, 1612346400, 1612350000, 1612353600, 1612357200,
1612360800, 1612364400, 1612368000, 1612371600, 1612375200, 1612378800,
1612382400, 1612386000, 1612389600, 1612393200, 1612396800, 1612400400,
1612404000, 1612407600, 1612411200, 1612414800, 1612418400, 1612422000,
1612425600, 1612429200, 1612432800, 1612436400, 1612440000, 1612443600,
1612447200, 1612450800, 1612454400, 1612458000, 1612461600, 1612465200,
1612468800, 1612472400, 1612476000, 1612479600, 1612483200, 1612486800,
1612490400, 1612494000, 1612497600, 1612501200, 1612504800, 1612508400,
1612512000, 1612515600, 1612519200, 1612522800, 1612526400, 1612530000,
1612533600, 1612537200, 1612540800, 1612544400, 1612548000, 1612551600,
1612555200, 1612558800, 1612562400, 1612566000, 1612569600, 1612573200,
1612576800, 1612580400, 1612584000, 1612587600, 1612591200, 1612594800,
1612598400, 1612602000, 1612605600, 1612609200, 1612612800, 1612616400,
1612620000, 1612623600, 1612627200, 1612630800, 1612634400, 1612638000,
1612641600, 1612645200, 1612648800, 1612652400, 1612656000, 1612659600,
1612663200, 1612666800, 1612670400, 1612674000, 1612677600, 1612681200,
1612684800, 1612688400, 1612692000, 1612695600, 1612699200, 1612702800,
1612706400, 1612710000, 1612713600, 1612717200, 1612720800, 1612724400,
1612728000, 1612731600, 1612735200, 1612738800, 1612742400, 1612746000,
1612749600, 1612753200, 1612756800, 1612760400, 1612764000, 1612767600,
1612771200, 1612774800, 1612778400, 1612782000, 1612785600, 1612789200,
1612792800, 1612796400, 1612800000, 1612803600, 1612807200, 1612810800,
1612814400, 1612818000, 1612821600, 1612825200, 1612828800, 1612832400,
1612836000, 1612839600, 1612843200, 1612846800, 1612850400, 1612854000,
1612857600, 1612861200, 1612864800, 1612868400, 1612872000, 1612875600,
1612879200, 1612882800, 1612886400, 1612890000, 1612893600, 1612897200,
1612900800, 1612904400, 1612908000, 1612911600, 1612915200, 1612918800,
1612922400, 1612926000, 1612929600, 1612933200, 1612936800, 1612940400,
1612944000, 1612947600, 1612951200, 1612954800, 1612958400, 1612962000,
1612965600, 1612969200, 1612972800, 1612976400, 1612980000, 1612983600,
1612987200, 1612990800, 1612994400, 1612998000, 1613001600, 1613005200,
1613008800, 1613012400, 1613016000, 1613019600, 1613023200, 1613026800,
1613030400, 1613034000, 1613037600, 1613041200, 1613044800, 1613048400,
1613052000, 1613055600, 1613059200, 1613062800, 1613066400, 1613070000,
1613073600, 1613077200, 1613080800, 1613084400, 1613088000, 1613091600,
1613095200, 1613098800, 1613102400, 1613106000, 1613109600, 1613113200,
1613116800, 1613120400, 1613124000, 1613127600, 1613131200, 1613134800,
1613138400, 1613142000, 1613145600, 1613149200, 1613152800, 1613156400,
1613160000, 1613163600, 1613167200, 1613170800, 1613174400, 1613178000,
1613181600, 1613185200, 1613188800, 1613192400, 1613196000, 1613199600,
1613203200, 1613206800, 1613210400, 1613214000, 1613217600, 1613221200,
1613224800, 1613228400, 1613232000, 1613235600, 1613239200, 1613242800,
1613246400, 1613250000, 1613253600, 1613257200, 1613260800, 1613264400,
1613268000, 1613271600, 1613275200, 1613278800, 1613282400, 1613286000,
1613289600, 1613293200, 1613296800, 1613300400, 1613304000, 1613307600,
1613311200, 1613314800, 1613318400, 1613322000, 1613325600, 1613329200,
1613332800, 1613336400, 1613340000, 1613343600, 1613347200, 1613350800,
1613354400, 1613358000, 1613361600, 1613365200, 1613368800, 1613372400,
1613376000, 1613379600, 1613383200, 1613386800, 1613390400, 1613394000,
1613397600, 1613401200, 1613404800, 1613408400, 1613412000, 1613415600,
1613419200, 1613422800, 1613426400, 1613430000, 1613433600, 1613437200,
1613440800, 1613444400, 1613448000, 1613451600, 1613455200, 1613458800,
1613462400, 1613466000, 1613469600, 1613473200, 1613476800, 1613480400,
1613484000, 1613487600, 1613491200, 1613494800, 1613498400, 1613502000,
1613505600, 1613509200, 1613512800, 1613516400, 1613520000, 1613523600,
1613527200, 1613530800, 1613534400, 1613538000, 1613541600, 1613545200,
1613548800, 1613552400, 1613556000, 1613559600, 1613563200, 1613566800,
1613570400, 1613574000, 1613577600, 1613581200, 1613584800, 1613588400,
1613592000, 1613595600, 1613599200, 1613602800, 1613606400, 1613610000,
1613613600, 1613617200, 1613620800, 1613624400, 1613628000, 1613631600,
1613635200, 1613638800, 1613642400, 1613646000, 1613649600, 1613653200,
1613656800, 1613660400, 1613664000, 1613667600, 1613671200, 1613674800,
1613678400, 1613682000, 1613685600, 1613689200, 1613692800, 1613696400,
1613700000, 1613703600, 1613707200, 1613710800, 1613714400, 1613718000,
1613721600, 1613725200, 1613728800, 1613732400, 1613736000, 1613739600,
1613743200, 1613746800, 1613750400, 1613754000, 1613757600, 1613761200,
1613764800, 1613768400, 1613772000, 1613775600, 1613779200, 1613782800,
1613786400, 1613790000, 1613793600, 1613797200, 1613800800, 1613804400,
1613808000, 1613811600, 1613815200, 1613818800, 1613822400, 1613826000,
1613829600, 1613833200, 1613836800, 1613840400, 1613844000, 1613847600,
1613851200, 1613854800, 1613858400, 1613862000, 1613865600, 1613869200,
1613872800, 1613876400, 1613880000, 1613883600, 1613887200, 1613890800,
1613894400, 1613898000, 1613901600, 1613905200, 1613908800, 1613912400,
1613916000, 1613919600, 1613923200, 1613926800, 1613930400, 1613934000,
1613937600, 1613941200, 1613944800, 1613948400, 1613952000, 1613955600,
1613959200, 1613962800, 1613966400, 1613970000, 1613973600, 1613977200,
1613980800, 1613984400, 1613988000, 1613991600, 1613995200, 1613998800,
1614002400, 1614006000, 1614009600, 1614013200, 1614016800, 1614020400,
1614024000, 1614027600, 1614031200, 1614034800, 1614038400, 1614042000,
1614045600, 1614049200, 1614052800, 1614056400, 1614060000, 1614063600,
1614067200, 1614070800, 1614074400, 1614078000, 1614081600, 1614085200,
1614088800, 1614092400, 1614096000, 1614099600, 1614103200, 1614106800,
1614110400, 1614114000, 1614117600, 1614121200, 1614124800, 1614128400,
1614132000, 1614135600, 1614139200, 1614142800, 1614146400, 1614150000,
1614153600, 1614157200, 1614160800, 1614164400, 1614168000, 1614171600,
1614175200, 1614178800, 1614182400, 1614186000, 1614189600, 1614193200,
1614196800, 1614200400, 1614204000, 1614207600, 1614211200, 1614214800,
1614218400, 1614222000, 1614225600, 1614229200, 1614232800, 1614236400,
1614240000, 1614243600, 1614247200, 1614250800, 1614254400, 1614258000,
1614261600, 1614265200, 1614268800, 1614272400, 1614276000, 1614279600,
1614283200, 1614286800, 1614290400, 1614294000, 1614297600, 1614301200,
1614304800, 1614308400, 1614312000, 1614315600, 1614319200, 1614322800,
1614326400, 1614330000, 1614333600, 1614337200, 1614340800, 1614344400,
1614348000, 1614351600, 1614355200, 1614358800, 1614362400, 1614366000,
1614369600, 1614373200, 1614376800, 1614380400, 1614384000, 1614387600,
1614391200, 1614394800, 1614398400, 1614402000, 1614405600, 1614409200,
1614412800, 1614416400, 1614420000, 1614423600, 1614427200, 1614430800,
1614434400, 1614438000, 1614441600, 1614445200, 1614448800, 1614452400,
1614456000, 1614459600, 1614463200, 1614466800, 1614470400, 1614474000,
1614477600, 1614481200, 1614484800, 1614488400, 1614492000, 1614495600,
1614499200, 1614502800, 1614506400, 1614510000, 1614513600, 1614517200,
1614520800, 1614524400, 1614528000, 1614531600, 1614535200, 1614538800,
1614542400, 1614546000, 1614549600, 1614553200, 1614556800, 1614560400,
1614564000, 1614567600, 1614571200, 1614574800, 1614578400, 1614582000,
1614585600, 1614589200, 1614592800, 1614596400, 1614600000, 1614603600,
1614607200, 1614610800, 1614614400, 1614618000, 1614621600, 1614625200,
1614628800, 1614632400, 1614636000, 1614639600, 1614643200, 1614646800,
1614650400, 1614654000, 1614657600, 1614661200, 1614664800, 1614668400,
1614672000, 1614675600, 1614679200, 1614682800, 1614686400, 1614690000,
1614693600, 1614697200, 1614700800, 1614704400, 1614708000, 1614711600,
1614715200, 1614718800, 1614722400, 1614726000, 1614729600, 1614733200,
1614736800, 1614740400, 1614744000, 1614747600, 1614751200, 1614754800,
1614758400, 1614762000, 1614765600, 1614769200, 1614772800, 1614776400,
1614780000, 1614783600, 1614787200, 1614790800, 1614794400, 1614798000,
1614801600, 1614805200, 1614808800, 1614812400, 1614816000, 1614819600,
1614823200, 1614826800, 1614830400, 1614834000, 1614837600, 1614841200,
1614844800, 1614848400, 1614852000, 1614855600, 1614859200, 1614862800,
1614866400, 1614870000, 1614873600, 1614877200, 1614880800, 1614884400,
1614888000, 1614891600, 1614895200, 1614898800), tzone = "UTC", class = c("POSIXct",
"POSIXt")), Débit_horaire = c(5.052, 5.036, 5.009, 4.982, 4.958,
4.937, 4.917, 4.885, 4.858, 4.834, 4.804, 4.786, 4.769, 4.753,
4.741, 4.722, 4.713, 4.702, 4.689, 4.68, 4.669, 4.664, 4.658,
4.645, 4.623, 4.595, 4.567, 4.539, 4.51, 4.48, 4.443, 4.413,
4.381, 4.352, 4.327, 4.318, 4.291, 4.27, 4.268, 4.268, 4.265,
4.257, 4.254, 4.258, 4.27, 4.283, 4.295, 4.299, 4.303, 4.307,
4.305, 4.308, 4.32, 4.334, 4.355, 4.396, 4.457, 4.531, 4.624,
4.738, 4.879, 5.057, 5.28, 5.558, 5.863, 6.186, 6.562, 6.958,
7.327, 7.555, 7.638, 7.638, 7.577, 7.452, 7.291, 7.089, 6.867,
6.646, 6.469, 6.301, 6.161, 6.043, 5.946, 5.872, 5.807, 5.752,
5.702, 5.67, 5.658, 5.65, 5.647, 5.656, 5.692, 5.74, 5.786, 5.839,
5.91, 6.003, 6.124, 6.256, 6.374, 6.489, 6.596, 6.686, 6.72,
6.725, 6.706, 6.684, 6.646, 6.61, 6.578, 6.568, 6.554, 6.54,
6.529, 6.535, 6.538, 6.542, 6.553, 6.531, 6.547, 6.54, 6.534,
6.51, 6.504, 6.486, 6.462, 6.444, 6.429, 6.412, 6.395, 6.373,
6.365, 6.354, 6.344, 6.334, 6.326, 6.315, 6.303, 6.295, 6.295,
6.298, 6.296, 6.298, 6.289, 6.273, 6.258, 6.238, 6.225, 6.219,
6.21, 6.213, 6.216, 6.216, 6.22, 6.222, 6.229, 6.233, 6.236,
6.239, 6.238, 6.248, 6.258, 6.271, 6.292, 6.311, 6.33, 6.342,
6.348, 6.358, 6.36, 6.365, 6.366, 6.359, 6.353, 6.342, 6.333,
6.327, 6.33, 6.327, 6.319, 6.326, 6.332, 6.324, 6.34, 6.356,
6.373, 6.402, 6.443, 6.487, 6.537, 6.571, 6.582, 6.582, 6.563,
6.54, 6.515, 6.478, 6.442, 6.41, 6.372, 6.331, 6.304, 6.277,
6.246, 6.218, 6.205, 6.199, 6.193, 6.186, 6.187, 6.203, 6.233,
6.274, 6.315, 6.362, 6.4, 6.432, 6.459, 6.484, 6.512, 6.539,
6.544, 6.548, 6.543, 6.529, 6.525, 6.593, 6.638, 6.713, 6.831,
6.968, 7.142, 7.37, 7.656, 7.924, 8.117, 8.181, 8.262, 8.273,
8.25, 8.243, 8.183, 8.13, 8.073, 8.021, 7.953, 7.888, 7.819,
7.765, 7.733, 7.703, 7.675, 7.663, 7.661, 7.673, 7.701, 7.739,
7.8, 7.843, 7.902, 7.973, 8.06, 8.136, 8.216, 8.342, 8.429, 8.585,
8.694, 8.838, 9.026, 9.38, 9.815, 10.294, 10.786, 11.347, 11.859,
12.233, 12.637, 12.966, 13.283, 13.685, 13.908, 14.334, 14.721,
15.149, 15.581, 16.521, 17.244, 17.842, 18.501, 19.313, 20.18,
20.831, 21.707, 22.559, 23.352, 24.222, 25.223, 25.933, 26.78,
27.336, 28.231, 28.845, 29.255, 29.805, 30.559, 30.458, 30.79,
30.01, 30.098, 29.579, 29.405, 29.149, 28.992, 28.879, 28.596,
28.513, 27.866, 27.839, 27.721, 27.259, 27.385, 26.951, 26.759,
26.467, 26.188, 25.971, 25.564, 25.572, 25.392, 25.243, 25.029,
24.91, 24.723, 24.44, 24.286, 24.039, 23.907, 23.594, 23.454,
23.31, 23.152, 22.881, 22.773, 22.481, 22.202, 21.956, 21.718,
21.385, 21.212, 20.804, 20.526, 20.251, 19.879, 19.599, 19.357,
19.033, 18.914, 18.647, 18.546, 18.301, 18.163, 17.975, 17.763,
17.563, 17.43, 17.19, 17.061, 16.821, 16.673, 16.518, 16.312,
16.137, 16.007, 15.833, 15.698, 15.528, 15.349, 15.195, 15.025,
14.867, 14.718, 14.57, 14.357, 14.224, 14.021, 13.917, 13.79,
13.584, 13.405, 13.267, 13.115, 13, 12.925, 12.786, 12.678, 12.518,
12.44, 12.342, 12.221, 12.138, 12.006, 11.919, 11.84, 11.776,
11.701, 11.605, 11.54, 11.484, 11.371, 11.321, 11.252, 11.177,
11.123, 11.066, 11.028, 10.961, 10.917, 10.842, 10.808, 10.706,
10.66, 10.588, 10.534, 10.496, 10.439, 10.434, 10.407, 10.393,
10.326, 10.289, 10.243, 10.188, 10.134, 10.09, 10.07, 10.039,
10.089, 10.19, 10.407, 10.695, 11.179, 11.769, 12.402, 13.126,
13.95, 14.598, 15.244, 15.748, 16.186, 16.655, 16.938, 17.177,
17.321, 17.365, 17.337, 17.256, 17.256, 17.163, 17.1, 17.143,
17.363, 17.495, 17.883, 18.542, 19.075, 19.628, 20.129, 20.61,
20.944, 21.508, 22.023, 22.557, 23.16, 23.827, 24.4, 24.849,
25.24, 25.387, 25.282, 25.309, 25.296, 25.562, 25.898, 26, 26.274,
26.225, 26.295, 26.394, 26.274, 26.071, 26.072, 26.035, 26.211,
26.383, 26.303, 26.501, 26.474, 26.513, 26.728, 26.825, 27.036,
27.121, 27.443, 27.65, 27.775, 27.689, 27.79, 28.197, 27.82,
28.144, 27.998, 27.789, 27.686, 26.934, 26.954, 26.612, 26.222,
26.192, 25.722, 25.616, 25.531, 25.292, 25.189, 24.797, 24.832,
24.664, 24.525, 24.343, 24.419, 24.284, 24.044, 24.054, 23.818,
23.651, 23.619, 23.587, 23.589, 23.397, 23.314, 23.144, 22.834,
22.846, 22.571, 22.437, 22.204, 22.036, 21.734, 21.588, 21.283,
21.018, 20.798, 20.394, 20.138, 19.926, 19.679, 19.477, 19.19,
18.914, 18.683, 18.514, 18.243, 18.11, 17.981, 17.873, 17.723,
17.655, 17.56, 17.496, 17.444, 17.353, 17.342, 17.289, 17.221,
17.182, 17.05, 16.966, 16.87, 16.649, 16.514, 16.457, 16.305,
16.172, 16.121, 16.223, 16.198, 16.412, 16.695, 16.984, 17.443,
17.808, 18.403, 19.015, 19.509, 19.919, 20.47, 20.922, 21.258,
21.561, 21.636, 21.557, 21.321, 21.223, 20.979, 20.834, 20.559,
20.501, 20.434, 20.312, 20.226, 20.08, 19.971, 19.846, 19.8,
19.712, 19.652, 19.59, 19.502, 19.442, 19.378, 19.261, 19.197,
19.193, 19.159, 19.119, 19.053, 18.966, 18.916, 18.877, 18.774,
18.71, 18.623, 18.501, 18.422, 18.277, 18.145, 18.057, 17.947,
17.828, 17.73, 17.56, 17.472, 17.347, 17.187, 17.019, 16.896,
16.784, 16.676, 16.496, 16.395, 16.255, 16.154, 16.125, 16.037,
15.981, 15.889, 15.897, 15.811, 15.786, 15.723, 15.584, 15.535,
15.433, 15.333, 15.291, 15.213, 15.091, 15.02, 14.928, 14.845,
14.804, 14.916, 15.406, 15.627, 16, 16.414, 16.809, 17.147, 17.457,
17.723, 17.973, 18.175, 18.371, 18.551, 18.613, 18.581, 18.389,
18.036, 17.58, 17.179, 16.751, 16.425, 16.129, 15.928, 15.791,
15.61, 15.487, 15.389, 15.363, 15.355, 15.312, 15.326, 15.301,
15.324, 15.291, 15.266, 15.184, 15.102, 15.056, 15.008, 14.947,
14.899, 14.84, 14.82, 14.819, 14.781, 14.766, 14.768, 14.715,
14.696, 14.631, 14.54, 14.455, 14.344, 14.209, 14.103, 14.027,
13.931, 13.848, 13.769, 13.662, 13.611, 13.493, 13.424, 13.358,
13.286, 13.232, 13.132, 13.034, 12.98, 12.937, 12.86, 12.76,
12.694, 12.604, 12.561, 12.466, 12.361, 12.257, 12.138, 12.025,
11.95, 11.863, 11.767, 11.675, 11.554, 11.473, 11.38, 11.287,
11.198, 11.125, 11.074, 11.007, 10.96, 10.906, 10.85, 10.768,
10.693, 10.62, 10.513, 10.435, 10.33, 10.226, 10.147, 10.045,
9.956, 9.844, 9.758, 9.669, 9.596, 9.542, 9.488, 9.453, 9.423,
9.359, 9.331, 9.332, 9.307, 9.279, 9.242, 9.204, 9.147, 9.079,
8.982, 8.892, 8.814, 8.74, 8.659, 8.602, 8.531, 8.45, 8.412,
8.35, 8.284, 8.243, 8.202, 8.168, 8.133, 8.111, 8.08, 8.062,
8.044, 8.024, 8.007, 7.975, 7.924, 7.867, 7.782, 7.71, 7.624,
7.544, 7.463, 7.373, 7.297, 7.233, 7.166, 7.103, 7.052, 7.024,
6.985, 6.938, 6.917, 6.914, 6.909, 6.893, 6.9, 6.903, 6.917,
6.891, 6.853, 6.803, 6.749, 6.694, 6.639, 6.565, 6.483, 6.42,
6.37, 6.32, 6.282, 6.252, 6.226, 6.204, 6.214, 6.215, 6.166,
6.155, 6.134, 6.133, 6.158, 6.175, 6.181, 6.175, 6.167, 6.148,
6.116, 6.082, 6.046, 6.019, 5.983, 5.962, 5.933, 5.912, 5.891,
5.864, 5.85, 5.831, 5.822, 5.806, 5.806, 5.813, 5.828, 5.856,
5.876, 5.907, 5.931, 5.97, 6.023, 6.055, 6.072, 6.069, 6.06,
6.052, 6.028, 6.015, 5.987, 5.965, 5.937, 5.902, 5.869, 5.836,
5.798, 5.77, 5.756, 5.767, 5.812, 5.869, 5.935, 6.029, 6.119,
6.188, 6.235, 6.292, 6.332, 6.383, 6.455, 6.575, 6.634, 6.617,
6.543, 6.441, 6.336, 6.241, 6.162, 6.08, 6.011, 5.942, 5.885,
5.83, 5.785, 5.756, 5.729, 5.691, 5.666, 5.628, 5.581, 5.531,
5.478, 5.431, 5.383, 5.327, 5.278, 5.23, 5.193, 5.159, 5.119,
5.086, 5.057, 5.034, 5.016, 4.995, 4.912, 4.963, 4.987, 5.019,
5.099, 5.21, 5.313, 5.476, 5.692, 5.883, 6.152, 6.457, 6.633,
6.623, 6.445, 6.218, 5.996, 5.813, 5.667, 5.548, 5.461, 5.379,
5.303, 5.24, 5.168, 5.122, 5.078, 5.044, 5.004, 4.973, 4.943,
4.911, 4.875, 4.848, 4.823, 4.794, 4.772, 4.75, 4.727, 4.711,
4.693, 4.668, 4.652, 4.639, 4.627, 4.617, 4.608, 4.593, 4.573,
4.56, 4.549, 4.544, 4.541, 4.532, 4.512, 4.504, 4.493, 4.474,
4.465, 4.45, 4.438, 4.417, 4.407, 4.396, 4.387, 4.381, 4.375,
4.361, 4.351, 4.337, 4.334, 4.33, 4.325, 4.32, 4.311, 4.312,
4.305, 4.291, 4.274, 4.257, 4.248, 4.233, 4.23, 4.222, 4.216,
4.215, 4.2, 4.19, 4.184, 4.177, 4.172, 4.161, 4.152, 4.145, 4.141,
4.136, 4.133, 4.126, 4.114, 4.099, 4.087, 4.078, 4.064, 4.05,
4.043, 4.035, 4.025, 4.013, 4.002, 3.989, 3.979, 3.97, 3.966,
3.958, 3.943, 3.94, 3.932, 3.928, 3.918, 3.91, 3.901, 3.88, 3.874,
3.866, 3.849, 3.831, 3.818, 3.804, 3.795, 3.787, 3.781, 3.779,
3.773, 3.767, 3.763, 3.757, 3.754, 3.751, 3.745, 3.738, 3.729,
3.731, 3.724, 3.723, 3.72, 3.72, 3.709, 3.707, 3.709, 3.707,
3.685, 3.668, 3.667, 3.682, 3.671, 3.652, 3.644, 3.635, 3.632,
3.626, 3.617, 3.614, 3.604, 3.598, 3.591, 3.586, 3.58, 3.578,
3.57, 3.564, 3.558, 3.547, 3.534, 3.524, 3.514, 3.499, 3.481,
3.476, 3.459, 3.449, 3.44, 3.43, 3.414, 3.41, 3.411, 3.417, 3.431,
3.455, 3.496, 3.53, 3.568, 3.604, 3.645, 3.685, 3.717, 3.728,
3.727, 3.69, 3.635, 3.592, 3.558, 3.52, 3.498, 3.472, 3.44, 3.413,
3.393, 3.37, 3.353, 3.321, 3.287, 3.261, 3.24, 3.237, 3.23, 3.227,
3.225, 3.223, 3.233, 3.242, 3.247, 3.234, 3.208, 3.181, 3.154,
3.134, 3.123, 3.109, 3.097, 3.091, 3.091, 3.085, 3.08, 3.074,
3.073, 3.07, 3.046, 3.052, 3.053, 3.049, 3.046, 3.029, 3.028,
3.018, 3.003, 2.997, 2.981, 2.971, 2.957, 2.946, 2.937, 2.931,
2.926, 2.916, 2.907, 2.904, 2.893, 2.887, 2.876, 2.866, 2.861,
2.854, 2.851, 2.85, 2.855, 2.865, 2.86, 2.859, 2.855, 2.843,
2.838, 2.828, 2.806, 2.793, 2.782, 2.775, 2.77, 2.759, 2.752,
2.744, 2.737, 2.729, 2.723, 2.719, 2.711, 2.703, 2.693, 2.697,
2.7, 2.699, 2.695, 2.693, 2.693, 2.692, 2.69, 2.681, 2.67, 2.658,
2.642, 2.637, 2.63, 2.623, 2.614, 2.611, 2.604, 2.604, 2.598,
2.591, 2.593, 2.594, 2.591, 2.585, 2.602, 2.601, 2.597, 2.59,
2.583, 2.582, 2.569, 2.562, 2.551, 2.544, 2.536, 2.537, 2.523,
2.516, 2.513, 2.515, 2.516, 2.516, 2.519, 2.518, 2.517, 2.516,
2.52, 2.534, 2.566, 2.607, 2.625, 2.675, 2.703, 2.742, 2.782,
2.827, 2.956)), class = c("tbl_df", "tbl", "data.frame"), row.names = c(NA,
-1297L))

You could set the size of the zoom panel relative to the main plot via the argument zoom.size which defaults to 2, i.e. the zoom panel is twice the size of the main panel. Hence, to achieve your desired result set zoom.size=.5:
require(dplyr)
require(tidyverse)
require(ggforce)
DebitH %>%
ggplot(aes(x = Date, y = Débit_horaire)) +
geom_point(alpha = 6 / 10, size = 0.3, color = "blue") +
geom_line(alpha = 4 / 10, size = 0.5, color = "blue") +
labs(x = "Date", y = "Débit Horaire (m3/s)") +
theme_bw() +
theme(
panel.grid.major.y = element_line(
color = "grey",
size = 0.25,
linetype = 2
),
legend.position = "none"
) +
facet_zoom(xlim = as.POSIXct(c("2021-01-15 00:00:00", "2021-02-15 00:00:00")), zoom.size = .5)

How to implement k-fold cross-validation while forcing linear regression of predicted to real values to 1:1 line

I'm trying to train y as a polynomial function of x so that when the predicted y values are linearly regressed against the real y values, the relationship is on the 1:1 line (diagram - The image on the right uses geom_smooth(method="lm") for demonstration, but with SMA from the lmodel2() function, the regression line is 1:1). I'm kind of a stats amateur so I'm aware there might be problems with this, but without forcing the model tends to overestimate low values and underestimate high values. My question is: How do I introduce k-fold cross-validation using an existing package like caret or cvms? It seems like they need a model object to be returned and I can't figure out how to code my problem like that. Is there some way I can train the model by minimizing my custom metric and still return a model object with ypred and use it in k-fold CV?
This is my code for calculating the coefficients without k-fold CV:
data <- data.frame(
x = c(1.514, 1.514, 1.825, 1.281, 1.118, 1.279, 1.835, 1.819, 0.462, 1.53, 1.004, 1.19, 1.275, 0.428, 0.313, 0.909, 0.995, 0.995, 0.706, 0.563, 0.827, 0.65, 0.747, 1.013, 1.013, 1.163, 1.091, 1.163, 1.091, 0.955, 0.955, 2.044, 2.044, 1.777, 1.777, 1.434, 1.393, 1.324, 0.981, 0.845, 1.595, 1.595, 1.517, 1.517, 1.403, 1.403, 0.793, 0.793, 1.016, 0.901, 0.847, 1.054, 0.877, 1.639, 1.639, 1.268, 1.268, 0.842, 0.842, 0.827, 0.777, 1.024, 1.238, 1.238, 1.702, 1.702, 0.673, 0.673, 1.256, 1.256, 0.898, 0.898, 0.66, 0.933, 0.827, 0.836, 1.122, 1.5, 1.5, 1.44, 1.44, 0.671, 0.671, 0.486, 0.486, 1.051, 1.051, 0.971, 0.538, 0.971, 0.538, 1.012, 1.012, 0.776, 0.776, 0.854, 0.854, 0.74, 0.989, 0.989),
y = c(0.19, 0.18, 0.816, 2.568, 0.885, 0.521, 0.268, 0.885, 4.781, 1.648, 0.989, 1.614, 1.492, 0.679, 2.256, 3.17, 1.926, 1.631, 0.462, 2.48, 0.658, 0.355, 0.373, 2.31, 3.263, 1.374, 1.374, 2.637, 2.637, 2.073, 2.298, 0.257, 0.292, 0.359, 0.329, 1.329, 1.272, 3.752, 1.784, 0.76, 0.458, 0.488, 0.387, 0.387, 3.401, 1.458, 8.945, 9.12, 0.308, 0.386, 0.405, 6.444, 3.17, 0.458, 0.47, 0.572, 0.589, 1.961, 1.909, 0.636, 0.32, 1.664, 0.756, 0.851, 0.403, 0.232, 23.112, 22.042, 0.745, 0.477, 2.349, 3.01, 0.39, 0.246, 0.43, 1.407, 1.358, 0.235, 0.215, 0.595, 0.685, 2.539, 2.128, 8.097, 5.372, 0.644, 0.626, 17.715, 17.715, 6.851, 6.851, 2.146, 1.842, 3.147, 2.95, 1.127, 1.019, 8.954, 0.796, 0.758),
stringsAsFactors = FALSE)
optim_results <- optim(par = c(a0 = 0.3, a1 = -3.8, a2 = -1, a3 = 1, a4 = 1),
fn = function (params, x, y) {
params <- as.list(params)
ypred <- with(params, (a0 + (a1*x) + (a2*x^2) + (a3*x^3) + (a4*x^4)))
mod <- suppressMessages(lmodel2::lmodel2(ypred ~ y))$regression.results[3,]
line <- mod$Slope * y + mod$Intercept
return(sum((y - line)^2))},
x = log10(data$x),
y = log10(data$y))
cf <- as.numeric(optim_results$par)
data <- data %>% dplyr::mutate(ypred = 10^(cf[1] + cf[2]*log10(x) + cf[3]*log10(x)^2 + cf[4]*log10(x)^3 + cf[5]*log10(x)^4))
str(data)

Great question!
cvms::cross_validate_fn() allows you to cross-validate custom functions. You just have to wrap your code in a model function and a predict function as so:
EDIT: Added extraction of model parameters from the optim() output. optim() returns a list, which we convert to a class and then tell coef() how to extract the coefficients for that class.
library(dplyr)
library(groupdata2)
library(cvms)
# Set seed for reproducibility
set.seed(2)
data <- data.frame(
x = c(1.514, 1.514, 1.825, 1.281, 1.118, 1.279, 1.835, 1.819, 0.462, 1.53, 1.004, 1.19, 1.275, 0.428, 0.313, 0.909, 0.995, 0.995, 0.706, 0.563, 0.827, 0.65, 0.747, 1.013, 1.013, 1.163, 1.091, 1.163, 1.091, 0.955, 0.955, 2.044, 2.044, 1.777, 1.777, 1.434, 1.393, 1.324, 0.981, 0.845, 1.595, 1.595, 1.517, 1.517, 1.403, 1.403, 0.793, 0.793, 1.016, 0.901, 0.847, 1.054, 0.877, 1.639, 1.639, 1.268, 1.268, 0.842, 0.842, 0.827, 0.777, 1.024, 1.238, 1.238, 1.702, 1.702, 0.673, 0.673, 1.256, 1.256, 0.898, 0.898, 0.66, 0.933, 0.827, 0.836, 1.122, 1.5, 1.5, 1.44, 1.44, 0.671, 0.671, 0.486, 0.486, 1.051, 1.051, 0.971, 0.538, 0.971, 0.538, 1.012, 1.012, 0.776, 0.776, 0.854, 0.854, 0.74, 0.989, 0.989),
y = c(0.19, 0.18, 0.816, 2.568, 0.885, 0.521, 0.268, 0.885, 4.781, 1.648, 0.989, 1.614, 1.492, 0.679, 2.256, 3.17, 1.926, 1.631, 0.462, 2.48, 0.658, 0.355, 0.373, 2.31, 3.263, 1.374, 1.374, 2.637, 2.637, 2.073, 2.298, 0.257, 0.292, 0.359, 0.329, 1.329, 1.272, 3.752, 1.784, 0.76, 0.458, 0.488, 0.387, 0.387, 3.401, 1.458, 8.945, 9.12, 0.308, 0.386, 0.405, 6.444, 3.17, 0.458, 0.47, 0.572, 0.589, 1.961, 1.909, 0.636, 0.32, 1.664, 0.756, 0.851, 0.403, 0.232, 23.112, 22.042, 0.745, 0.477, 2.349, 3.01, 0.39, 0.246, 0.43, 1.407, 1.358, 0.235, 0.215, 0.595, 0.685, 2.539, 2.128, 8.097, 5.372, 0.644, 0.626, 17.715, 17.715, 6.851, 6.851, 2.146, 1.842, 3.147, 2.95, 1.127, 1.019, 8.954, 0.796, 0.758),
stringsAsFactors = FALSE)
# Fold data
# Will do 10-fold repeated cross-validation (10 reps)
data <- fold(
data = data,
k = 10, # Num folds
num_fold_cols = 10 # Num repetitions
)
# Write a model function from your code
# This ignores the formula and hyperparameters but
# you could pass values through those if you wanted
# to try different formulas or hyperparameter values
model_fn <- function(train_data, formula, hyperparameters){
out <- optim(par = c(a0 = 0.3, a1 = -3.8, a2 = -1, a3 = 1, a4 = 1),
fn = function (params, x, y) {
params <- as.list(params)
ypred <- with(params, (a0 + (a1*x) + (a2*x^2) + (a3*x^3) + (a4*x^4)))
mod <- suppressMessages(lmodel2::lmodel2(ypred ~ y))$regression.results[3,]
line <- mod$Slope * y + mod$Intercept
return(sum((y - line)^2))},
x = log10(train_data$x),
y = log10(train_data$y))
# Convert output to an S3 class
# so we can extract parameters with coef()
class(out) <- "OptimModel"
out
}
# Tell coef() how to extract the parameters
# This can modified if you need more info from the optim() output
# Just return a named list
coef.OptimModel <- function(object) {
object$par
}
# Write a predict function from your code
predict_fn <- function(test_data, model, formula, hyperparameters, train_data){
cf <- as.numeric(model$par)
test_data %>%
dplyr::mutate(
ypred = 10^(cf[1] + cf[2]*log10(x) + cf[3]*log10(x)^2 + cf[4]*log10(x)^3 + cf[5]*log10(x)^4)
) %>%
.[["ypred"]]
}
# Cross-validate the model
cv <- cross_validate_fn(
data = data,
model_fn = model_fn,
predict_fn = predict_fn,
formulas = c("y ~ x"), # Not currently used by the model function
fold_cols = paste0('.folds_', seq_len(10)),
type = 'gaussian'
)
#> Will cross-validate 1 models. This requires fitting 100 model instances.
# Check output
cv
# A tibble: 1 × 17
Fixed RMSE MAE NRMSE(I…¹ RRSE RAE RMSLE Predic…² Results Coeffi…³ Folds
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <list> <list> <list> <int>
1 x 4.00 2.31 2.66 1.47 1.17 0.662 <tibble> <tibble> <tibble> 100
# … with 6 more variables: `Fold Columns` <int>, `Convergence Warnings` <int>,
# `Other Warnings` <int>, `Warnings and Messages` <list>, Process <list>,
# Dependent <chr>, and abbreviated variable names ¹​`NRMSE(IQR)`,
# ²​Predictions, ³​Coefficients
# ℹ Use `colnames()` to see all variable names
Created on 2022-10-15 with reprex v2.0.2

Run Forecasting model with multiple Dependent and Independent variables in R

I have a data set with 7 features including the date column where my dependent variables are NORTH and YORKSANDTHEHUMBER and the rest are independent variables. I want to automate the process where I take my first dependent feature NORTH and run it against all the independent variables in a univariate manner so that the first model gives me the result for NORTH and x1, second for NORTH and x2 and so on via using for loop but I couldn't make the sense. Can anyone please guide me in this?
Data:
structure(list(Date = structure(c(289094400, 297043200, 304992000,
312854400, 320716800, 328665600, 336614400, 344476800, 352252800,
360201600, 368150400, 376012800, 383788800, 391737600, 399686400,
407548800, 415324800, 423273600, 431222400, 439084800, 446947200,
454896000, 462844800, 470707200, 478483200, 486432000, 494380800,
502243200, 510019200, 517968000, 525916800, 533779200, 541555200,
549504000, 557452800, 565315200, 573177600, 581126400, 589075200,
596937600, 604713600, 612662400, 620611200, 628473600, 636249600,
644198400, 652147200, 660009600, 667785600, 675734400, 683683200,
691545600, 699408000, 707356800, 715305600, 723168000, 730944000,
738892800, 746841600, 754704000, 762480000, 770428800, 778377600,
786240000, 794016000, 801964800, 809913600, 817776000, 825638400,
833587200, 841536000, 849398400, 857174400, 865123200, 873072000,
880934400, 888710400, 896659200, 904608000, 912470400, 920246400,
928195200, 936144000, 944006400, 951868800, 959817600, 967766400,
975628800, 983404800, 991353600, 999302400, 1007164800, 1014940800,
1022889600, 1030838400, 1038700800, 1046476800, 1054425600, 1062374400,
1070236800, 1078099200, 1086048000, 1093996800, 1101859200, 1109635200,
1117584000, 1125532800, 1133395200, 1141171200, 1149120000, 1157068800,
1164931200, 1172707200, 1180656000, 1188604800, 1196467200, 1204329600,
1212278400, 1220227200, 1228089600, 1235865600, 1243814400, 1251763200,
1259625600, 1267401600, 1275350400, 1283299200, 1291161600, 1298937600,
1306886400, 1314835200, 1322697600, 1330560000, 1338508800, 1346457600,
1354320000, 1362096000, 1370044800, 1377993600, 1385856000, 1393632000,
1401580800, 1409529600, 1417392000, 1425168000, 1433116800, 1441065600,
1448928000, 1456790400, 1464739200, 1472688000, 1480550400, 1488326400,
1496275200, 1504224000, 1512086400, 1519862400, 1527811200, 1535760000,
1543622400, 1551398400, 1559347200, 1567296000, 1575158400, 1583020800,
1590969600, 1598918400, 1606780800, 1614556800, 1622505600, 1630454400,
1638316800), class = c("POSIXct", "POSIXt"), tzone = "UTC"),
Industrialproduction = c(8.2, 8.79, 0.94, 1.53, -3.18, -8.66,
-8.96, -11.93, -8.14, -4.5, 1.53, 2.06, 2.39, 2.02, 2.01,
1.68, 2.16, 2.15, 3.77, 5.95, 3.58, 0.81, -1.58, -1.72, 3.62,
9.78, 8.51, 3.49, 1.97, -1.02, 1.92, 6.13, 3.87, 3.54, 2.76,
4.19, 4.73, 4.84, 6.64, 3.88, 2.05, 1.36, 0.53, 1.47, 1.61,
3.22, -1.45, -2.76, -3.83, -5.06, -4.01, -1.76, -0.27, -0.82,
2.23, 0.69, 1.38, 2.07, 2.32, 4.1, 4.61, 5.68, 6.13, 5.91,
2.85, 1.66, 1, 0.37, 2.52, 1.26, 1.24, 1.48, 0.37, 2.24,
2.7, 4.38, 7.6, 3.89, 0.84, -0.82, -0.46, 5.61, 9.48, 5.06,
1.95, 2.1, 1.08, 6.27, 1.46, 2.28, 3.21, 3.37, 12.94, -1.06,
-2.07, -6.22, -5.19, 6.65, 6.78, 4.35, -2.69, -1.31, -2.08,
3.44, -3.08, -0.92, -1.62, -0.91, 8.32, 2.57, 4.33, 2.44,
1.52, -1.3, -4.94, -3.97, -3.59, -1.83, 1.77, -1.86, -4.86,
-5.07, -7.55, -5.37, -0.33, -1.2, -0.11, -1.11, -8.39, -5.4,
-5.52, -4.16, 0.12, -0.7, -0.58, -0.59, 0.48, 3.87, 5.29,
7.91, 7.21, -0.45, -2.23, -1.86, 4.19, 5.9, 5.94, 2.45, 0,
-0.75, -1.08, 1.63, -3.28, -0.22, 3.49, 1.07, 1.53, 5.3,
4.21, 6.14, 10.24, 2.26, 0.71, -1.3, -8.9, -12.36, -5.02,
-2.83, 3.76, 9.86, 1.9, 0.94), Householdconsumption = c(30.09,
32.53, 33.35, 35.23, 37.18, 37.59, 38.89, 39.82, 41.56, 42.7,
43.74, 45.03, 46.19, 46.95, 48.29, 49.84, 51.26, 52.15, 53.5,
54.36, 55.4, 56.7, 57.05, 58.88, 60.09, 61.44, 63.27, 64.74,
66.63, 68.35, 69.55, 70.81, 72.3, 74.29, 76.65, 78.82, 81.51,
83.81, 86.53, 88.4, 90.29, 92.46, 93.95, 95.99, 97.85, 100.83,
102.42, 104.05, 106.08, 107.79, 109.33, 110.63, 111.71, 113.52,
114.9, 116.02, 118.31, 119.4, 122.27, 124.05, 125.13, 125.99,
127.59, 129.19, 130.16, 132.29, 135.06, 136.61, 139.34, 142.14,
144.59, 146.95, 149.43, 151.71, 155.34, 156.37, 158.39, 160.69,
164.47, 164.41, 167.54, 169.48, 170.09, 172.51, 176.26, 177.61,
179.44, 180.28, 182.96, 184.01, 186.83, 186.34, 188.79, 190.18,
191.94, 194.56, 196.46, 198.86, 201.75, 203.09, 205.24, 208.26,
210.84, 213.9, 216.18, 217.54, 220.61, 222.9, 223.67, 227.66,
230.62, 232.57, 234.8, 237.82, 241.91, 244.47, 248.84, 248.63,
248.14, 243.9, 241.46, 239.04, 240.72, 243.03, 241.87, 248,
249.95, 251.91, 254.92, 254.81, 257.17, 261.11, 262.28, 265.29,
266.74, 271.42, 274.28, 277.61, 282.48, 282.94, 285.76, 290.21,
292.88, 294.9, 296.07, 299.14, 302.58, 302.82, 309.63, 313.2,
318.64, 320.87, 323.41, 325.57, 326.56, 329.67, 335.95, 337.61,
341.08, 345.09, 346.16, 350.18, 350.23, 347.89, 339.85, 270.86,
325.65, 320.28, 311.3, 341.24, 354.61, 361.47), Investmentgrowth = c(17.3,
22.73, 25.8, 29.99, 21.59, 15.49, 11.11, 6.04, 4.23, 4.42,
4.28, 3.51, 6.53, 8.81, 10.52, 12.63, 14.6, 8.04, 7.42, 10.72,
11.15, 16.11, 15.45, 11.36, 18.41, 8.32, 8.99, 8.18, 0.86,
5.04, 9.07, 14.27, 11.11, 19.61, 23.14, 19.47, 27.16, 24.6,
17.45, 16.17, 20.57, 17.01, 17.76, 15.36, 8.28, 7.05, 2.92,
2.83, -3.08, -4.32, -7.48, -6.69, -3.71, -4.64, -3.87, -4.88,
-1.72, -0.38, 1.97, 4.65, 2.84, 2.98, 3.68, 2.88, 0.69, 3.5,
4.91, 5.66, 11.3, 13.85, 10.87, 4.01, -5.63, -8.06, -3.81,
3.94, 10.74, 9.14, 3.83, 3.36, 3.29, 3.24, 7.59, 3.43, 7.05,
13.14, 1.12, 7.68, 4.22, 1.34, 9.27, 0.78, 0.66, -1.52, 4.17,
12.34, 11.74, 5.2, 1.89, -1.56, 2.26, 5.89, 5.79, 4.84, 3.44,
7.15, 7.27, 7.31, 6.11, 5.7, 8.15, 6.96, 7.79, 10.05, 2.71,
9.61, 4.63, 2.72, 1.13, -6.1, -8.98, -14.36, -9.8, -11.41,
-3.13, 1.28, 3.81, 9.18, 1.62, 2.05, 2.14, 2.03, 7.32, 3.88,
0.09, 3.44, -1.27, 6.8, 10.41, 5.73, 12.93, 7.89, 6.8, 7.92,
8.2, 9.32, 6.18, 7.39, 5.22, 6.07, 9.44, 5.64, 6.8, 7.2,
4.77, 6.83, 3.74, 1.63, 2.59, 1.17, 4.39, 3.28, 3.78, 2.18,
-1.93, -19.78, -7.51, -2.54, -0.99, 23.33, 6.54, 4.25), ConsumerPriceIndex = c(24.88,
25.94, 27.55, 28.28, 29.79, 31.39, 31.92, 32.55, 33.55, 34.94,
35.55, 36.48, 37.02, 38.14, 38.14, 38.45, 38.73, 39.54, 40.1,
40.49, 40.76, 41.57, 41.99, 42.35, 43.25, 44.46, 44.46, 44.74,
45.06, 45.58, 45.81, 46.42, 46.88, 47.49, 47.72, 48.14, 48.44,
49.43, 49.83, 50.33, 50.82, 52.02, 52.42, 53.11, 53.91, 55.6,
56.69, 57.09, 57.59, 60.27, 60.67, 61.27, 61.67, 62.56, 62.56,
62.86, 63.16, 64.05, 64.45, 64.35, 64.55, 65.35, 65.45, 65.64,
66.24, 67.04, 67.34, 67.63, 68.03, 68.63, 68.93, 69.13, 69.13,
69.82, 70.22, 70.32, 70.7, 71.3, 71.5, 71.8, 71.9, 72.3,
72.4, 72.6, 72.3, 72.9, 73.1, 73.2, 73, 74.1, 74.1, 74, 74.1,
74.6, 74.8, 75.2, 75.3, 75.4, 75.9, 76.2, 76.1, 76.6, 76.7,
77.4, 77.5, 78.1, 78.6, 78.9, 78.9, 80.1, 80.5, 81.3, 81.4,
82, 81.9, 83, 83.4, 85.2, 86.1, 85.5, 85.8, 86.7, 87.1, 88,
88.7, 89.5, 89.8, 91.2, 92.2, 93.3, 94.4, 95.1, 95.4, 95.5,
96.5, 97.6, 98.1, 98.3, 99.1, 99.6, 99.7, 100.2, 100.3, 100.1,
99.7, 100.2, 100.2, 100.3, 100.2, 100.6, 101.1, 101.9, 102.7,
103.5, 104.3, 105, 105.1, 105.9, 106.6, 107.1, 107, 107.9,
108.4, 108.5, 108.6, 108.8, 109.2, 109.4, 109.7, 111.4, 112.4,
114.7), NORTH = c(4.06976744186047, 5.51675977653633, 7.2799470549305,
4.75015422578655, 4.59363957597172, 3.15315315315317, 1.2008733624454,
-0.377562028047452, -0.108283703302655, 0.650406504065032,
0.969305331179318, 0.106666666666688, 3.09003729355352, 2.11886304909562,
2.32793522267207, 5.68743818001977, -1.46934955545156, 3.95611702127658,
5.19438987619354, -0.0912012507600199, 2.81677896109541,
3.97412590369087, 1.30118326353028, 3.31553807249226, 1.32872294960955,
2.93700394923507, 0.908853875665812, 1.81241002546971, -1.3414545718222,
4.81772747317361, -3.4743890895067, 4.63823913990992, 0.857370960463727,
1.78620594713658, 0.527472527472524, -4.05973562947765, -0.136726966764838,
3.16657890117607, 5.95161125667812, 8.01002055498458, 10.5501040737437,
13.4138468987035, 2.93371279497212, 8.84291046495554, -6.87764606265876,
2.90741287990725, 3.71548486856639, 1.23317430567388, -1.1153443739474,
4.31313207880924, -1.64273763383666, 0.751373343751978, -3.21877014345816,
1.16314882913623, -3.59065232516701, -4.65283582701413, 4.98489115166134,
3.18459755147199, -3.72875180849018, 2.20137289784552, -4.22488416879167,
-0.706371260732776, -2.33320725244584, -2.77596063540517,
9.48636128308308, -2.15172116987927, -5.71766285746257, 1.92271571537407,
0.655934629757954, 4.01517293049256, -2.89270965830984, 3.910032505864,
-1.31616434600239, 1.51533020314829, 3.09793915477058, 1.00146317751519,
-0.516295759142123, 4.36356154298765, -0.254418667464494,
-1.38015492270122, -0.375369475589906, 3.79511767246943,
1.67693295616696, 0.197127124553074, -1.01758464617007, 5.70477696100394,
-1.37564670926045, 1.39335708665185, 2.29473337483174, -1.40489357721877,
10.7514355294201, -0.403985348024547, -0.0106181613732362,
10.6504339189417, 7.72602065226992, 6.66622841015428, 7.3618861388054,
7.20852539277177, 7.17954849482943, 5.47999408979134, 9.96115783870405,
6.960515961579, 4.82626274289161, -0.428385428540776, 1.6283388103162,
2.07440844957785, -0.707412409361252, -4.9247119657169, 4.3311229522328,
2.53158682305453, -0.8800288960527, 2.40275362264064, 0.67520264383003,
3.97711266595697, 0.00749650524863867, -0.990038901876062,
-0.63991866618197, -2.00199671222057, -5.15098853828302,
-3.65317386916235, -4.67277715297035, -0.564594703469009,
3.29526766976492, 0.0888482310529472, -0.524228981506815,
3.04012050839788, -1.53185447929528, -0.338917708381546,
-2.5450727924491, 3.36238295093309, -0.918735392055365, -0.766840492430499,
-0.767135363240273, 0.0468961039030733, 1.51618073336643,
-2.02356670927575, -1.11584500803018, 2.45568937824186, 0.989863990072745,
-0.4214032191629, 2.8219393653178, 4.51474479784726, -2.49049271581373,
-0.41346860604498, 3.13864420514751, -0.0877964623534655,
-0.674347043417658, -0.143267961613368, -0.243406512930108,
0.0402054219496719, 0.12912750657269, 0.168664845016241,
-0.713623226415894, 1.49163339466038, 1.57747101133233, -2.10536689354583,
3.12980292320487, -0.90833324273064, -1.71375697178543, 0.582188469928239,
2.89692448021907, 0.0768238907010953, -1.53392147948349,
1.23622644511851, -0.0506227154778281, 0.327869614383542,
2.62019966395382, 3.48629495563575, 0.593740862165774, 4.09560684327741,
2.32207959691005, 0.506809670097958), YORKSANDTHEHUMBER = c(4.0121120363361,
5.45851528384282, 9.52380952380951, 6.04914933837431, 3.03030303030299,
5.42099192618225, 2.78993435448577, -0.53219797764768, 1.97966827180309,
1.15424973767052, 0.466804979253115, -1.96179659266907, 2.42232754081095,
0.719794344473031, -0.306278713629415, 3.37941628264209,
2.74393263992076, 3.91920555341303, 1.91585099967527, 0.892125625853447,
2.91888477848958, 3.78293078507868, 0.109815847271484, 6.83486625601216,
0.722691730511011, 3.56008625759656, -0.227160867754524,
2.69419041475355, -1.17134094520194, 2.78546324684064, 1.01487759630426,
1.54843356139717, 4.15602836879435, 4.43619773934357, -0.309698451507728,
-1.45519947678222, -1.09839057574248, 9.08267346664877, 11.8913598474363,
13.9511229623114, 9.71243848306475, 7.66524473371739, 6.46801731884651,
-2.26736490763654, -4.35729847494552, -2.93870179974964,
-7.72353426221536, -7.01127302722023, 2.02543627323513, 2.51245245873873,
0.712134856164617, -2.74951902189779, 3.20525370229387, -2.17225212432703,
0.304311135936791, -5.21962007478405, -1.22771231792975,
5.62676205566459, -0.0988236572110239, 0.865912760888606,
-3.71050647202427, 1.5475703474865, -3.43233328040058, -2.86288061069106,
-0.551968808874026, 2.05442655433966, 0.388675938226524,
-2.60493926554792, -2.23312255163324, 5.04817095211292, 1.43656632546456,
2.53687507970646, -2.37376845704496, 4.95419269721737, 2.5486061891899,
-0.64046817419928, 1.75846231104579, 0.542834308795226, -0.322606591645488,
-2.67961743436791, 3.57498650723638, 2.89743475977992, 1.28567849851333,
1.828392232888, -0.335580970541442, 5.34860062451308, -2.98213938289875,
3.55468980520775, 2.76514398982056, 3.45832186518539, 1.32470422187813,
2.79428923624948, 3.8093136923264, 9.02544568216825, 7.65854560247412,
11.0775256253873, -0.658987130155868, 10.726463566155, 5.35747018223358,
4.66387144397987, 5.14763674355188, 10.581371911713, 3.46926043870116,
-0.000369065205607915, 0.924675325682334, 3.681119585314,
-0.0731638011738147, 0.690177922935143, 1.33427941484383,
2.65734876034112, 1.62515008951355, 1.48038293242949, 0.494192527588077,
2.39510739408179, 0.818557817036399, -1.1083492547105, -1.89465779498896,
-3.74953204588813, -3.7238074999174, -4.9788025925358, -4.65464963206228,
3.34588197167384, 2.20886725349025, 1.99954661835316, -0.777545762347822,
3.58681336123701, -2.96757202302368, -3.36310924643208, 2.01483012871867,
2.4154475314586, -0.642314624781054, -2.0920093049768, -1.73904001349183,
1.69071701857513, 0.201962934561265, -2.66472457335063, 0.323680874793625,
1.37879437405697, 3.26467995053582, 2.21645486418079, -0.646736928898328,
2.06516965491332, 1.8250141624007, -1.68545096699093, -0.818973277015041,
4.05215303886115, -1.16233786449552, -1.56747999678074, 0.67708495662531,
2.92754908797974, 1.50505329502891, -1.12667258046976, -0.765034978617734,
2.67854615526131, -0.306294171526678, 0.175047038539941,
1.56451236885344, 0.618844724791642, 3.34585295985361, -1.76420421213768,
-0.079420811764984, 1.56942028744185, 0.407910173531572,
-0.268243129544691, 2.57107118459526, -0.758721256899304,
3.03713057699041, 2.68699850192726, 1.88666482868311, 4.78697689266296,
2.43248653386118, 1.27252711337855)), row.names = c(NA, -172L
), class = "data.frame")
Code:
library(tseries)
library(dplyr)
# ARDL MODELING AND FORECASTING
in_sampleARDL <- data %>%
dplyr::filter(Date < '2020-03-01')
out_sampleARDL <-data %>%
dplyr::filter(Date >= '2020-03-01')
auto_ardl(NORTH~Householdconsumption,
data = in_sampleARDL, max_order = 4, selection = 'BIC')
pred1 <-forecast(ardlDlm(formula = NORTH ~ diff(Householdconsumption),
data = in_sampleARDL, p =3)
, x =out_sampleARDL$NORTH, h = 4)
error1 = out_sampleARDL$NORTH[1:2]- pred1[["forecasts"]]
mean(error1^2)
auto_ardl(NORTH~Industrialproduction,
data = in_sampleARDL, max_order = 4, selection = 'BIC')
pred2 <-forecast(ardlDlm(formula = NORTH ~ Industrialproduction,
data = in_sampleARDL, p =3)
, x =out_sampleARDL$NORTH, h = 4)
error2 = out_sampleARDL$NORTH[1:4]- pred2[["forecasts"]]
mean(error2^2)

How to fit a regression of information (negative entropy) ~ size in R?

I would like to fit a regression to negative entropy ~ size data in order to estimate the optimum size (pointed with the arrow).
The range of entropy data is between 0 and 1, while the range of size data goes from x > 0 to ∞. The information value here was computed following Information = Hmax - H using Shannon
An example of the data is:
size <- c(0.0010, 0.0035, 0.0060, 0.0085, 0.0110, 0.0135, 0.0160, 0.0185, 0.0210, 0.0235, 0.0260, 0.0285, 0.0310, 0.0335, 0.0360, 0.0385, 0.0410, 0.0435, 0.0460, 0.0485, 0.0510, 0.0535, 0.0560, 0.0585, 0.0610, 0.0635, 0.0660, 0.0685, 0.0710, 0.0735, 0.0760, 0.0785, 0.0810, 0.0835, 0.0860, 0.0885, 0.0910, 0.0935, 0.0960, 0.0985, 0.1010, 0.1035, 0.1060, 0.1085, 0.1110, 0.1135, 0.1160, 0.1185, 0.1210, 0.1235, 0.1260, 0.1285, 0.1310, 0.1335, 0.1360, 0.1385, 0.1410, 0.1435, 0.1460, 0.1485, 0.1510, 0.1535, 0.1560, 0.1585, 0.1610, 0.1635, 0.1660, 0.1685, 0.1710, 0.1735, 0.1760, 0.1785, 0.1810, 0.1835, 0.1860, 0.1885, 0.1910, 0.1935, 0.1960, 0.1985, 0.2010, 0.2035, 0.2060, 0.2085, 0.2110, 0.2135, 0.2160, 0.2185, 0.2210, 0.2235, 0.2260, 0.2285, 0.2310, 0.2335, 0.2360, 0.2385, 0.2410, 0.2435, 0.2460, 0.2485, 0.2510, 0.2535, 0.2560, 0.2585, 0.2610, 0.2635, 0.2660, 0.2685, 0.2710, 0.2735, 0.2760, 0.2785, 0.2810, 0.2835, 0.2860, 0.2885, 0.2910, 0.2935, 0.2960, 0.2985, 0.3010, 0.3035, 0.3060, 0.3085, 0.3110, 0.3135, 0.3160, 0.3185, 0.3210, 0.3235, 0.3260, 0.3285, 0.3310, 0.3335, 0.3360, 0.3385, 0.3410, 0.3435, 0.3460, 0.3485, 0.3510, 0.3535, 0.3560, 0.3585, 0.3610, 0.3635, 0.3660, 0.3685, 0.3710, 0.3735, 0.3760, 0.3785, 0.3810, 0.3835, 0.3860, 0.3885, 0.3910, 0.3935, 0.3960, 0.3985, 0.4010, 0.4035, 0.4060, 0.4085, 0.4110, 0.4135, 0.4160, 0.4185, 0.4210, 0.4235, 0.4260, 0.4285, 0.4310, 0.4335, 0.4360, 0.4385, 0.4410, 0.4435, 0.4460, 0.4485, 0.4510, 0.4535, 0.4560, 0.4585, 0.4610, 0.4635, 0.4660, 0.4685, 0.4710, 0.4735, 0.4760, 0.4785, 0.4810, 0.4835, 0.4860, 0.4885, 0.4910, 0.4935, 0.4960, 0.4985)
information <- c(0.001, 0.136, 0.366, 0.532, 0.642, 0.719, 0.773, 0.810, 0.839, 0.854, 0.871, 0.878, 0.882, 0.885, 0.885, 0.886, 0.884, 0.878, 0.877, 0.873, 0.867, 0.864, 0.847, 0.851, 0.839, 0.839, 0.836, 0.828, 0.822, 0.821, 0.817, 0.817, 0.805, 0.805, 0.791, 0.796, 0.798, 0.795, 0.799, 0.788, 0.787, 0.785, 0.779, 0.775, 0.769, 0.771, 0.772, 0.769, 0.770, 0.746, 0.777, 0.755, 0.755, 0.752, 0.744, 0.745, 0.745, 0.759, 0.740, 0.747, 0.740, 0.747, 0.740, 0.738, 0.745, 0.718, 0.732, 0.748, 0.714, 0.731, 0.744, 0.710, 0.720, 0.750, 0.725, 0.708, 0.715, 0.753, 0.720, 0.702, 0.722, 0.708, 0.701, 0.716, 0.723, 0.719, 0.695, 0.692, 0.701, 0.720, 0.719, 0.699, 0.709, 0.699, 0.703, 0.714, 0.706, 0.686, 0.698, 0.694, 0.703, 0.708, 0.698, 0.653, 0.676, 0.687, 0.697, 0.707, 0.689, 0.691, 0.666, 0.646, 0.660, 0.687, 0.706, 0.722, 0.714, 0.702, 0.654, 0.642, 0.647, 0.650, 0.663, 0.673, 0.703, 0.704, 0.698, 0.694, 0.655, 0.641, 0.620, 0.625, 0.631, 0.644, 0.655, 0.663, 0.691, 0.669, 0.674, 0.647, 0.644, 0.659, 0.657, 0.652, 0.649, 0.636, 0.619, 0.613, 0.609, 0.629, 0.655, 0.667, 0.652, 0.640, 0.636, 0.643, 0.640, 0.652, 0.649, 0.645, 0.657, 0.654, 0.650, 0.622, 0.614, 0.617, 0.612, 0.621, 0.627, 0.622, 0.616, 0.626, 0.615, 0.624, 0.634, 0.633, 0.631, 0.629, 0.614, 0.617, 0.630, 0.633, 0.629, 0.620, 0.629, 0.626, 0.614, 0.624, 0.608, 0.591, 0.606, 0.607, 0.605, 0.618, 0.610, 0.622, 0.618, 0.616, 0.613, 0.612)
It seems (please correct me) that the information data follows a Maxwell-Boltzmann distribution
require(shotGroups)
plot(information ~ log(size))
lines(pMaxwell(information, sigma= 0.3639920) ~ log(size), col = "red")
However, I am not sure how to estimate this optimum value using a parameter in a regression or if there is any other approach to determine this optimum rather than max(information).
Any thoughts?

This works OK, although I had to limit the upper bound of the root-finding function below the region where the spline starts to wiggle ...
library(splines)
ss <- smooth.spline(log(size),information,spar=0.4)
uu <- uniroot(function(x) predict(ss,x=x,deriv=1)$y,interval=c(-5,-3))
Result is -3.29.
Picture:
plot(information ~log(size))
lines(ss$x,ss$y,col="red",lwd=2)
abline(v=uu$root,col="blue")

I cannot place an image in a comment, and so place it here. Using the example data in your post, I got an OK fit to the equation "y = a*pow(x,b+c/x)" with parameters a = 5.3705331969760373E-01, b = -1.8691263532001362E-01 and c = 1.5557275459064772E-03 yielding an R-squared of 0.9770 and RMSE of 0.0156

Find point of systematic decrease in R

I have the following data frame:
df <- structure(list(x = c(1059.6, 1061.4, 1063.4, 1064.9, 1066.3,
1068, 1069.8, 1071.4, 1072.9, 1074.4, 1075.9, 1077.5, 1079.1,
1080.5, 1082.1, 1083.8, 1085.1, 1086.7, 1088.1, 1089.5, 1091.6,
1093.1, 1094.5, 1095.8, 1097.1, 1098.4, 1099.8, 1101.1, 1102.5,
1103.9, 1105.3, 1106.6, 1108, 1109.4, 1110.8, 1112.2, 1113.7,
1115.2, 1116.5, 1117.9, 1119.1, 1120.4, 1121.8, 1123.1, 1124.8,
1126.2, 1127.4, 1128.8, 1130.2, 1131.8, 1133.3, 1134.6, 1138.5,
1141.2, 1142.4, 1143.6, 1144.8, 1146.8, 1148.2, 1149.6, 1150.9,
1152.2, 1153.4, 1154.7, 1155.9, 1157.1, 1158.3, 1159.5, 1161.9,
1163.4, 1164.7, 1166, 1167.2, 1169, 1170.3, 1171.5, 1172.8, 1173.9,
1175.1, 1176.8, 1178, 1179.2, 1180.3, 1181.6, 1182.8, 1184.1,
1185.8, 1187, 1188.2, 1189.4, 1190.5, 1191.8, 1193, 1194.3, 1195.5,
1205.8, 1206.9, 1208, 1209, 1210.2, 1211.3, 1212.4, 1213.6, 1214.7,
1217.2, 1218.6, 1222.3, 1223.6, 1224.7, 1225.9, 1227.1, 1228.2,
1229.3, 1230.4, 1231.6, 1232.7, 1233.6, 1234.6, 1235.7, 1236.9,
1238.4, 1239.5, 1240.6, 1241.6, 1242.7, 1243.7, 1244.8, 1245.9,
1247, 1248.1, 1249.2, 1250.3, 1251.3, 1252.6, 1253.7, 1254.8,
1255.8, 1256.8, 1257.8, 1258.8, 1261.4, 1262.5, 1263.5, 1264.5,
1265.6, 1266.6, 1267.8, 1268.8, 1270.1, 1271.1, 1272.1, 1273.2,
1274.1, 1275.2, 1276.3, 1279, 1280, 1281, 1282.1, 1283.1, 1284.1,
1285, 1286, 1287, 1288, 1289, 1290, 1291.1, 1292.3, 1293.3, 1294.4,
1298.6, 1299.6, 1300.5, 1301.5, 1302.5, 1303.5, 1304.6, 1305.5,
1306.4, 1307.6, 1308.6, 1309.7, 1310.7, 1311.7, 1312.7, 1315.2,
1316.3, 1317.3, 1318.3, 1319.3, 1320.3, 1321.3, 1322.3, 1323.2,
1326.8, 1327.8, 1329, 1330, 1331, 1332, 1333, 1333.9, 1335, 1336,
1337.3, 1338.3, 1339.3, 1340.5, 1341.6, 1342.7, 1343.8, 1344.9,
1345.9, 1346.8, 1347.8, 1348.8, 1350, 1351.1, 1352, 1353.3, 1354.3,
1355.3, 1356.2, 1357.1, 1358, 1359.2, 1360.2, 1364.4, 1365.5,
1366.6, 1367.6, 1368.7, 1369.8, 1371, 1372, 1373, 1374.1, 1375,
1376, 1376.9, 1377.8, 1378.7, 1379.6, 1380.5, 1381.4, 1382.3,
1383.3, 1384.2, 1385.2, 1387.6, 1388.5, 1389.5, 1390.4, 1391.4,
1392.5, 1393.6, 1394.6, 1395.6, 1397, 1397.9, 1398.8, 1399.8,
1400.6, 1401.6, 1402.5, 1403.4, 1404.2, 1405.1, 1407.4, 1408.3,
1409.2, 1410.1, 1411.2, 1412.2, 1413.2, 1414.2, 1415.6, 1416.7,
1417.8, 1418.9, 1420.2, 1421.5, 1424.6, 1425.7, 1427, 1428.1,
1429.3, 1430.7, 1431.9, 1433.1, 1434.5, 1435.7, 1436.8, 1438,
1439.4, 1440.6, 1441.9, 1443, 1444.4, 1445.6, 1447.3, 1448.5,
1449.7, 1450.9, 1452.1, 1453.2, 1454.5, 1455.6, 1456.8, 1458.1,
1459.3, 1460.3, 1461.4, 1462.4, 1463.9, 1465.1, 1466.3, 1469.8,
1471.1, 1472.6, 1473.8, 1475, 1476.2, 1477.5, 1479.1, 1480.7,
1482, 1483.2, 1484.9, 1486.2, 1487.5, 1488.8, 1490, 1491.3, 1492.4,
1503, 1504.3, 1506.3, 1507.5, 1508.8, 1510.2, 1511.4, 1512.5,
1513.8, 1515.6, 1517.1, 1520.1, 1523.9, 1526.5, 1527.9, 1529.8,
1531.2, 1532.4, 1533.7, 1536, 1537.4, 1538.8, 1540.2, 1541.5,
1542.9, 1544.2, 1545.6, 1546.9, 1548.3, 1549.7, 1551.1, 1552.7,
1554.1, 1556.4, 1557.8, 1559.2, 1560.6, 1562, 1563.4, 1564.7,
1566.2, 1567.5, 1568.9, 1570.2, 1571.4, 1573.9, 1576.7, 1581.5,
1582.8, 1584.7, 1586.2, 1587.7, 1589.3, 1591, 1592.8, 1594.7,
1596.4, 1598.5, 1600.6, 1602.4, 1604.6, 1606.9, 1609, 1611, 1612.6,
1614.4, 1616.3, 1618.6, 1620.6, 1622.4, 1624.5, 1627.2, 1629.3,
1631.4, 1635, 1636.9, 1638.6, 1640.5, 1642.1, 1643.7, 1645.5,
1647.1, 1648.7, 1650.9, 1653, 1655.2, 1657.1, 1659.1, 1661.5,
1663.6, 1665.9, 1668.1, 1671.7, 1674, 1676.2, 1678.1, 1679.7,
1681.6, 1683.6, 1685.7, 1688, 1693.7, 1695.7, 1697.6, 1699.7,
1701.7, 1704.1), y = c(1.876, 2.027, 2.087, 2.231, 2.18, 1.922,
1.921, 1.851, 1.961, 2.035, 2.043, 2.043, 1.838, 2.032, 2.112,
1.976, 2.046, 2.117, 2.062, 2.07, 1.748, 1.917, 2.092, 2.283,
2.158, 2.119, 2.023, 1.971, 1.882, 2.058, 2.141, 2.241, 2.079,
1.946, 1.959, 2.117, 1.923, 2.015, 2.066, 1.98, 2.091, 1.929,
1.987, 1.852, 1.935, 2.127, 1.982, 2.182, 2.099, 2.03, 1.912,
1.998, 2.491, 2.359, 2.188, 1.965, 1.906, 1.772, 1.927, 2.077,
2.381, 2.191, 2.089, 2.086, 2.017, 2.028, 1.832, 1.88, 2.053,
2.177, 1.995, 2.045, 2.116, 1.961, 1.99, 2.227, 2.235, 2.208,
2.249, 1.992, 2.045, 2.152, 2.237, 2.239, 2.247, 2.114, 1.956,
2.042, 1.926, 2.396, 2.184, 2.208, 2.016, 2.177, 2.29, 2.469,
2.502, 2.115, 2.081, 2.091, 2.188, 2.118, 2.179, 2.067, 1.962,
2.181, 2.246, 2.526, 2.145, 1.961, 2.299, 2.306, 2.34, 2.133,
1.974, 1.997, 2.47, 2.24, 2.247, 2.137, 1.965, 2.232, 2.225,
2.417, 2.362, 2.155, 2.034, 2.151, 2.176, 2.183, 2.372, 2.145,
2.284, 1.967, 2.299, 2.299, 2.183, 2.292, 2.193, 2.249, 2.32,
2.333, 2.286, 2.216, 2.233, 2.453, 2.373, 2.284, 2.074, 2.014,
2.153, 2.353, 2.465, 2.373, 2.181, 2.424, 2.334, 2.349, 2.39,
2.513, 2.526, 2.268, 2.098, 2.326, 2.385, 2.306, 2.378, 2.126,
2.191, 2.363, 2.222, 2.723, 2.686, 2.4, 2.251, 2.121, 2.104,
2.16, 2.333, 2.151, 2.116, 2.136, 2.293, 2.281, 2.313, 2.374,
2.585, 2.521, 2.656, 2.66, 2.399, 2.442, 2.413, 2.528, 2.212,
2.58, 2.667, 2.153, 2.736, 2.486, 2.406, 2.39, 2.403, 2.504,
2.502, 2.158, 2.617, 2.434, 2.364, 2.497, 2.456, 2.263, 2.432,
2.562, 2.453, 2.249, 2.18, 2.141, 2.324, 2.176, 2.184, 2.153,
2.332, 2.202, 2.332, 2.125, 2.156, 2.189, 2.71, 2.458, 2.502,
2.285, 2.527, 2.437, 2.418, 2.507, 2.087, 2.321, 2.701, 2.486,
2.389, 2.335, 2.26, 2.108, 2.164, 2.286, 2.103, 2.257, 2.137,
2.076, 2.378, 2.637, 2.446, 2.448, 2.539, 2.253, 2.099, 2.59,
2.405, 2.219, 2.542, 2.532, 2.507, 2.439, 2.463, 2.342, 2.329,
2.436, 2.511, 2.557, 2.603, 2.5, 2.428, 2.204, 2.307, 2.174,
2.193, 1.793, 2.116, 2.107, 2.209, 1.967, 1.834, 2.713, 2.647,
2.379, 2.229, 2.11, 1.964, 1.985, 2.162, 1.996, 2.074, 1.994,
1.839, 1.838, 1.743, 1.668, 1.91, 1.735, 1.714, 1.421, 1.767,
1.816, 1.755, 1.755, 1.698, 1.608, 1.556, 1.511, 1.394, 1.425,
1.579, 1.495, 1.627, 1.305, 1.471, 1.469, 1.67, 1.697, 1.42,
1.483, 1.274, 1.341, 1.235, 1.295, 1.401, 1.463, 1.313, 1.176,
1.333, 1.373, 1.299, 1.086, 1.139, 1.237, 1.303, 1.143, 1.13,
1.114, 1.096, 1.248, 1.302, 1.19, 1.069, 1.1, 1.027, 0.897, 1.09,
0.922, 1.116, 0.963, 1.011, 1.053, 1.025, 0.985, 0.981, 1.025,
1.117, 1.141, 1.135, 1.068, 0.982, 1.028, 1.06, 1.004, 1.112,
1.108, 1.04, 0.857, 0.91, 0.98, 1.081, 1.025, 0.996, 0.931, 1,
1.074, 0.987, 0.996, 1.125, 0.9, 0.607, 1.17, 1.08, 1, 0.909,
0.841, 0.924, 0.818, 0.846, 0.732, 1.006, 0.717, 0.594, 0.786,
0.685, 0.619, 0.684, 0.69, 0.633, 0.564, 0.689, 0.555, 0.445,
0.696, 0.677, 0.729, 0.541, 0.362, 0.312, 0.568, 0.711, 0.515,
0.622, 0.583, 0.631, 0.645, 0.696, 0.535, 0.424, 0.469, 0.519,
0.511, 0.485, 0.436, 0.412, 0.351, 0.556, 0.255, 0.519, 0.399,
0.497, 0.477, 0.564, 0.462, 0.433, 0.616, 0.547, 0.42, 0.499,
0.415, 0.368)), row.names = c(NA, -443L), class = c("tbl_df",
"tbl", "data.frame"), .Names = c("x", "y"))
Plot:
And I need to find the point that y starts to systematically decrease.
I know that the real point is x == 1405. However, is there a way to automatically detect it?
I am not expecting to find the exact x point. A really good approximation would do the job.
I already tried to perform a break point analysis with the segmented package, but with not much success. The best number I could get was x == 1363, but I am looking for a closer approximation.

Here's how to get a fitted smooth of the data using loess. When you say "starts to systematically decrease," I think you mean something like "when the slope gets negative beyond a certain threshold," since it seems to me that it visually peaks and starts to decline around the 1350's. I could manually get the peak to occur later by smoothing more than default, using span = 0.4.
library(broom)
fit <- loess(y ~ x, df, span = 0.4)
df_aug <- augment(fit)
Using that model, the peak looks to be around the 1370's.
library(dplyr); library(ggplot2)
df_aug %>% filter(.fitted == max(.fitted))
# # A tibble: 1 x 5
# y x .fitted .se.fit .resid
# <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 2.09 1373 2.39 0.0181 -0.307
I presume you could get a better result if you can more definitively describe what model should be used to define "systematically decrease."
You might alternately extract the slope and acceleration from the loess curve, but it's not clear that'd get you much closer you your expected result:
# Extract slope & acceleration
df_aug_slope <- df_aug %>%
mutate(slope = (.fitted - lag(.fitted)) /
(x - lag(x)),
curve = (slope - lag(slope)) /
(x - lag(x)))
ggplot(df_aug_slope, aes(x)) +
geom_point(aes(y=y)) +
geom_line(aes(y=.fitted), color ="red") +
geom_line(aes(y= slope * 100), color = "blue") +
geom_line(aes(y= curve * 1000), color = "green") +
geom_vline(xintercept = 1405, lty = "dashed") +
theme_minimal()

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