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Of these below 3 models output , though model 3 has a insignificant value in it , it has higher r square value and lesser F stat compare to model 2. In Model 2 though both variables are significant, the F statistic and RMSE value(1.638) is slightly higher than my model 3 (rms3 is 1.636). Which model should I consider here and why ? Can someone shed some light on this pleaes

 - model 1

    Call:
    lm(formula = tr$Sales ~ TV + Facebook, data = tr)
    Residuals:
        Min      1Q  Median      3Q     Max 
    -8.6942 -1.4420 -0.1152  1.4358  7.8306 
    Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
    (Intercept) 5.757673   0.571084  10.082  < 2e-16 ***
    TV          0.049902   0.002789  17.893  < 2e-16 ***
    Facebook    0.036963   0.010863   3.403  0.00086 ***
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    Residual standard error: 2.963 on 147 degrees of freedom
    Multiple R-squared:  0.6983,    Adjusted R-squared:  0.6942 
    F-statistic: 170.1 on 2 and 147 DF,  p-value: < 2.2e-16

model 2

summary(lfit2)

Call:
lm(formula = tr$Sales ~ TV + Adwords, data = tr)
Residuals:
    Min      1Q  Median      3Q     Max 
-8.5129 -0.5817  0.1659  1.1445  2.7496 
Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 2.926869   0.334627   8.747 4.68e-15 ***
TV          0.047292   0.001564  30.246  < 2e-16 ***
Adwords     0.180630   0.009500  19.015  < 2e-16 ***
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.655 on 147 degrees of freedom
Multiple R-squared:  0.9059,    Adjusted R-squared:  0.9046 
F-statistic: 707.7 on 2 and 147 DF,  p-value: < 2.2e-16

model 3

summary(lfit3)

Call:
lm(formula = tr$Sales ~ TV + Facebook + Adwords, data = tr)
Residuals:
    Min      1Q  Median      3Q     Max 
-8.6240 -0.6014  0.1477  1.1314  2.8010 
Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  2.991331   0.354757   8.432    3e-14 ***
TV           0.047312   0.001568  30.180   <2e-16 ***
Facebook    -0.003618   0.006486  -0.558    0.578    
Adwords      0.182602   0.010157  17.978   <2e-16 ***
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.659 on 146 degrees of freedom
Multiple R-squared:  0.9061,    Adjusted R-squared:  0.9042 
F-statistic: 469.7 on 3 and 146 DF,  p-value: < 2.2e-16
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The $R^2$ values of model 2 and 3 are essentially identical. Adding a variable always increases $R^2$ (technically, it could leave it exactly unchanged, but that is nearly impossible). In model 3, Facebook is adding almost nothing to the model

It looks like Adwords and Facebook are colinear, as well.

Given this, the simple solution is to use model 2. A more complicated solution is to try to combine Adwords and Facebook into one variable or to try ridge regression.

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  • $\begingroup$ thanks for your suggestion.. model 2 rmse is (slightly) more than model 3. Is it something like in conjunction with the good R2 values the rmse should also be lesser ? In the meanwhile, let me try the other options suggested by you. $\endgroup$ – raja ram Mar 14 '16 at 15:20
  • $\begingroup$ Yes. Adding even a nonsense variable will decrease RMSE slightly. $\endgroup$ – Peter Flom - Reinstate Monica Mar 15 '16 at 10:45

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