# Comparing the results of different Multiple Linear Regression analyses with a same dependent variable

I am trying to identify what combination of independent variables (5 variables) explain a dependent variable and I have a few questions:

1) Is it possible to use multiple linear regression analyses to identify what independent variables predict the dependent variable and discard some variables? In this case, is it O.K to say that variables “a”, “e” and probably “d” are the variables that best explain the dependent variable?

R = 0,898 Rsqr = 0,806 Adj Rsqr = 0,709

                Coefficient Std. Error  t  P    VIF
Constant       0,312  0,056    5,53    <0,001
Variable a    -0,001  0,001   -0,865    0,407 1,640
Variable b     0,000  0,000    3,928    0,003 1,546
Variable c     0,092  0,130    0,707    0,496 1,185
Variable d     0,077  0,037    2,058    0,067 1,795
Variable e     0,001  0,000    3,312    0,008 1,724


Analysis of Variance: DF SS MS F P

Regression 5 I 0,122 I 0,024 I 8,326 I 0,002

Residual 10 I 0,029 I 0,003

Total 15 I 0,151 I 0,010

2) Is it possible to identify what combination of variables are the best to predict the dependent variables? I mean, can I use the R2 values or the F-values to identify whether variables “b”, “d”, and “e” are better than variables “b” and “e” only to predict the dependent variable (based on the R2 values)? If so, what would be the best approach to do this, use the R2 values only or using any approach like AIC?

Multiple linear regression using variables b, d, and e:

R = 0,888 Rsqr = 0,788 Adj Rsqr = 0,735

            Coefficient Std. Error   t    P     VIF
Constant    0,317   0,050   6,287     <0,001
Variable b  0,000   0,000   4,060     0,002 1,512
Variable d  0,079   0,036   2,216     0,047 1,788
Variable e  0,001   0,000   3,482     0,005 1,280


Analysis of Variance: DF SS MS F P

Regression I 3 I 0,119 I 0,040 I 14,903 I <0,001

Residual I 12 I 0,032 I 0,003

Total I 15 I 0,151 I 0,010

Multiple linear regression using variables b and e:

R = 0,838 Rsqr = 0,702 Adj Rsqr = 0,656

            Coefficient Std. Error  t     P     VIF
Constant    0,416       0,0263      15,843  <0,001
Variable b  0,000767    0,000308    2,489   0,027   1,082
Variable d  0,000118    0,0000217   5,433   <0,001  1,082


Analysis of Variance: DF SS MS F P

Regression 2 0,106 0,0530 15,296 <0,001

Residual 13 0,0450 0,00346

Total 15 0,151 0,0101

Thanks!