How to choose first variable to do forward selection with (using p)?

Question

I have four variables, and I'm supposed to forward select (using their p values) them at the 5% level. Normally you'd probably start with the variable that has the lowest p value, but I have some confusing output on R.

This is what summary() does to my model when all variables are included i.e. Heat = yint + A + B + C+ D:

            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  96.0803    12.1436   7.912 4.73e-05 ***
A             1.1577     0.2268   5.105 0.000924 ***
B             0.1843     0.1339   1.376 0.206003    
C            -0.3649     0.1928  -1.892 0.095087 .  
D            -0.4719     0.1312  -3.596 0.007024 ** 

From this output, which gives the p value given that all other variables are in the model, we have A as the lowest p-value var at p = 0.000924.

However, when I use those variables in their own model D actually has the lowest p value (p of D = 0.000576 vs p of A = 0.00455):

summary(lm(Heat~D)):

            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 117.5679     5.2622  22.342 1.62e-10 ***
D            -0.7382     0.1546  -4.775 0.000576 ***

summary(lm(Heat~A)):

            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  81.4793     4.9273   16.54 4.07e-09 ***
A             1.8687     0.5264    3.55  0.00455 ** 

So would I be using A as my first variable or D as my first variable to forward select the rest with? My guess would be D since you don't start with the full model when forward selecting, but I have no idea what I'm doing.

Thanks

Answer 1

According to this, you should choose variable D as the first variable to add to the model. Start by considering all the models with a single variable and add the varibale whose inclusion gives the most statistically significant improvement of the fit.