Custom regression equation in R - r

Question

I have a set of data in R and I want to run a regression to test for correlation using custom coefficients.
Example:
x = lm(a ~ b + c + d, data=data, weights=weights)
That gives me coefficients for b, c, and d, but I just want to give b, c, and d my own coefficients and find, for example, the r^2. How would I do so?

Answer 1

Let's assume your predetermined coefficients are a three-element, numeric vector named: vec and that none of a,b,c are factors or character vectors:
#edit ... add a sum() function
(x = lm(a ~ 1, data=data, offset=apply(data, 1, function(x) {sum( c(1,x) * vec))} )
This should produce a model that has the specified estimates. You will probably need to do this:
summary(x)
As always... if you want tested code, then provide a dataset for testing. With the mtcars dataframe:
m1 = lm(mpg ~ carb + wt, data=mtcars)
vec <- coef(m1)
(x = lm(mpg ~ 1, data=mtcars,
offset=apply( mtcars[c("carb","wt")], 1,
function(x){ sum( c(1,x) *vec)} )))
Call:
lm(formula = mpg ~ 1, data = mtcars, offset = apply(mtcars[c("carb",
"wt")], 1, function(x) {
sum( c(1, x) * vec)
}))
Coefficients:
(Intercept)
-7.85e-17
So the offset model (with the coefficients used in the offset) is essentially an exact fit to the m1 model.

Answer 2

#BondedDust's method will be more efficient in the long run, but just for illustration, here's a simple example of how to create your own function to calculate R-squared for any regression coefficients you choose. We'll use the mtcars data set, which is built into R.
Assume a regression model that predicts "mpg" using the independent variables "carb" and "wt". a, b, and c are the three regression parameters that we need to provide to the function.
# Function to calculate R-squared
R2 = function(a,b,c) {
# Calculate the residual sum of squares from the regression model
SSresid = sum(((a + b*mtcars$carb + c*mtcars$wt) - mtcars$mpg)^2)
# Calculate the total sum of squares
SStot = sum((mtcars$mpg - mean(mtcars$mpg))^2)
# Calculate and return the R-squared for the regression model
return(1 - SSresid/SStot)
}
Now let's run the function. First let's see if our function matches the R-squared calculated by lm. We'll do this by creating a regression model in R, then we'll use the coefficients from that model and calculate the R-squared using our function and see if it matches the output from lm:
# Create regression model
m1 = lm(mpg ~ carb + wt, data=mtcars)
summary(m1)
Call:
lm(formula = mpg ~ carb + wt, data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-4.5206 -2.1223 -0.0467 1.4551 5.9736
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.7300 1.7602 21.435 < 2e-16 ***
carb -0.8215 0.3492 -2.353 0.0256 *
wt -4.7646 0.5765 -8.265 4.12e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.839 on 29 degrees of freedom
Multiple R-squared: 0.7924, Adjusted R-squared: 0.7781
F-statistic: 55.36 on 2 and 29 DF, p-value: 1.255e-10
From the summary, we can see that the R-squared is 0.7924. Let's see what we get from the function we just created. All we need to do is feed our function the three regression coefficients listed in the summary above. We can hard-code those numbers, or we can extract the coefficients from the model object m1 (which is what I've done below):
R2(coef(m1)[1], coef(m1)[2], coef(m1)[3])
[1] 0.7924425
Now let's calculate the R-squared for other choices of the regression coefficients:
a = 37; b = -1; c = -3.5
R2(a, b, c)
[1] 0.5277607
a = 37; b = -2; c = -5
R2(a, b, c)
[1] 0.0256494
To check lots of values of a parameter at once, you can, for example, use sapply. The code below will return the R-squared for values of c ranging from -7 to -3 in increments of 0.1 (with the other two parameters set to the the values returned by lm:
sapply(seq(-7,-3,0.1), function(x) R2(coef(m1)[1],coef(m1)[2],x))