I have 10000 samples. There are 4 independent variables and 1 dependent variable.
The independent variables are all centered with 0 mean.
I found the correlation coefficients between each of these variables which are as below:
I used linear regression model and below is the summary of that model:
Now, based on the coefficients of the predictor variables in the linear regression model, I have been asked to find the significant predictor (s).
Based on just the correlation values, I was thinking X 4 will be the significant predictor but its regression coefficient says a different story altogether. (x4 has the least coefficient value in lm summary output). Can you help me understand what exactly is the correct way to identify the significant predictor (s)?
Also, Additionally even if I remove the x4 variable from the lm model, the Residual standard error remains the same which kinda re-iterates the fact the it is not a significant predictor? Is
my understanding correct here?
Also, I ran the VarImp function available in R which again returned a smaller value for x4.
> varImp(lm_df, scale = TRUE) Overall x1 33.673993 x2 34.858260 x3 33.820908 x4 1.969445