How to fix a exponential regression to positively skewed data? - r
file linki am trying to explore exponential regression for predicting #calls_to_be_made(DV) for given #sales_potential(IDV) of customers.The data is positively skewed. is it better to try exponential regression for this case.? if so how to proceed? if not why? Need some more ideas.
I have to performed linear regression to predict #calls_to_be_made(DV) for given #sales_potential(IDV) of customers.The data is positively skewed. I have eliminated zero values and i have log10 transformed both the variables to get near normal distribution. it gave an rsqr value of 55%.
The expected result is how to perform exponential regression and also need clarity of thought on which model (technique) is good to prefer for my particular problem.?
#importdata
file1<-read.xlsx("wx2.xlsx",sheetName = "Sheet1",header = T)
str(file1)
#file1$Potential.18.19<-round(file1$Potential.18.19,digits = 0)
data1<-file1
data1$Sales_to_be_made <- log10(data1$Sales_to_be_made)
data1$calls_to_be_made <- log10(data1$calls_to_be_made)
dput(data1)
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ZLFPS is:
ZLFPS<-c(27.06,25.31,24.1,23.34,22.35,21.66,21.23,21.02,20.77,20.11,20.07,19.7,19.64,19.08,18.77,18.44,18.24,18.02,17.61,17.58,16.98,19.43,18.29,17.35,16.57,15.98,15.5,15.33,14.87,14.84,14.46,14.25,14.17,14.09,13.82,13.77,13.76,13.71,13.35,13.34,13.14,13.05,25.11,23.49,22.51,21.53,20.53,19.61,19.17,18.72,18.08,17.95,17.77,17.74,17.7,17.62,17.45,17.17,17.06,16.9,16.68,16.65,16.25,19.49,18.17,17.17,16.35,15.68,15.07,14.53,14.01,13.6,13.18,13.11,12.97,12.96,12.95,12.94,12.9,12.84,12.83,12.79,12.7,12.68,27.41,25.39,23.98,22.71,21.39,20.76,19.74,19.49,19.12,18.67,18.35,18.15,17.84,17.67,17.65,17.48,17.44,17.05,16.72,16.46,16.13,23.07,21.33,20.09,18.96,17.74,17.16,16.43,15.78,15.27,15.06,14.75,14.69,14.69,14.6,14.55,14.53,14.5,14.25,14.23,14.07,14.05,29.89,27.18,25.75,24.23,23.23,21.94,21.32,20.69,20.35,19.62,19.49,19.45,19,18.86,18.82,18.19,18.06,17.93,17.56,17.48,17.11,23.66,21.65,19.99,18.52,17.22,16.29,15.53,14.95,14.32,14.04,13.85,13.82,13.72,13.64,13.5,13.5,13.43,13.39,13.28,13.25,13.21,26.32,24.97,23.27,22.86,21.12,20.74,20.4,19.93,19.71,19.35,19.25,18.99,18.99,18.88,18.84,18.53,18.29,18.27,17.93,17.79,17.34,20.83,19.76,18.62,17.38,16.66,15.79,15.51,15.11,14.84,14.69,14.64,14.55,14.44,14.29,14.23,14.19,14.17,14.03,13.91,13.8,13.58,32.91,30.21,28.17,25.99,24.38,23.23,22.55,20.74,20.35,19.75,19.28,19.15,18.25,18.2,18.12,17.89,17.68,17.33,17.23,17.07,16.78,25.9,23.56,21.39,20.11,18.66,17.3,16.76,16.07,15.52,15.07,14.6,14.29,14.12,13.95,13.89,13.66,13.63,13.42,13.28,13.27,13.13,24.21,22.89,21.17,20.06,19.1,18.44,17.68,17.18,16.74,16.07,15.93,15.5,15.41,15.11,14.84,14.74,14.68,14.37,14.29,14.29,14.27,18.97,17.59,16.05,15.49,14.51,13.91,13.45,12.81,12.6,12,11.98,11.6,11.42,11.33,11.27,11.13,11.12,11.11,10.92,10.87,10.87,28.61,26.4,24.22,23.04,21.8,20.71,20.47,19.76,19.38,19.18,18.55,17.99,17.95,17.74,17.62,17.47,17.25,16.63,16.54,16.39,16.12,21.98,20.32,19.49,18.2,17.1,16.47,15.87,15.37,14.89,14.52,14.37,13.96,13.95,13.72,13.54,13.41,13.39,13.24,13.07,12.96,12.95,27.6,25.68,24.56,23.52,22.41,21.69,20.88,20.35,20.26,19.66,19.19,19.13,19.11,18.89,18.53,18.13,17.67,17.3,17.26,17.26,16.71,19.13,17.76,17.01,16.18,15.43,14.8,14.42,14,13.8,13.67,13.33,13.23,12.86,12.85,12.82,12.75,12.61,12.59,12.59,12.45,12.32)
QPZL<-c(36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16)
ZLDBFSAO<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2)
My model is:
fit32=lm(log(ZLFPS) ~ poly(QPZL,2,raw=T) + ZLDBFSAO)
results3 <- coef(summary(fit32))
first3<-as.numeric(results3[1])
second3<-as.numeric(results3[2])
third3<-as.numeric(results3[3])
fourth3<-as.numeric(results3[4])
fifth3<-as.numeric(results3[5])
#inverse model used for prediction of FPS
f1 <- function(x) {first3 +second3*x +third3*x^2 + fourth3*1}
You can see my dataset here. This dataset contains the values that I have to predict. The FPS variation per QP is heterogenous. See dataset. I added a new column.
The fitted dataset is a different one.
To test the model just write exp(f1(selected_QP)) where selected QP varies from 16 to 36. See the given dataset for QP values and the FPS value that the model should predict.
You can run the model online here.
When I'm using QP values in the middle, let's say between 23 and 32 the model predicts the FPS value pretty well. Otherwise, the prediction has big error value.
Regarding the linear regression model I should use Weighted Least Squares as a Solution to Heteroskedasticity of the fitted dataset. For references, see here, here and here. fit32=lm(log(ZLFPS) ~ poly(QPZL,2,raw=T) + ZLDBFSAO, weights=1/(1+0.5*QPZL^2)) The other code remains the same. This model gives me lower prediction error than the previous.