model 1: Call: lm(formula = qualified ~ weight + relate, data = data) Residuals:

Question

model 1:

Call:
lm(formula = qualified ~ weight + relate, data = data)

Residuals:
    Min      1Q Median      3Q     Max
-3.6765 -1.1235 -0.1235 0.8765 2.8765

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)   4.7408     0.4249 11.157   <2e-16 ***
weight        0.4887     0.1963   2.489   0.0137 *
relate        0.4470     0.1960   2.281   0.0238 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.294 on 173 degrees of freedom
Multiple R-squared: 0.06565,   Adjusted R-squared: 0.05485
F-statistic: 6.078 on 2 and 173 DF, p-value: 0.002811

model 2:

Call:
lm(formula = qualified ~ weight:relate, data = data)

Residuals:
    Min      1Q Median      3Q     Max
-3.7857 -1.0714 -0.0714 0.9286 2.9286

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)    5.50000    0.22591 24.346   <2e-16 ***
weight:relate 0.28571    0.08539   3.346    0.001 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.294 on 174 degrees of freedom
Multiple R-squared: 0.06046,   Adjusted R-squared: 0.05506
F-statistic: 11.2 on 1 and 174 DF, p-value: 0.001004

which one is better and why ?

Explanation / Answer

We always choose the model which has larger adjusted R square.

It increases only when the regressor contributes significantly to the mode.

model 1 Adjusted R square 5.485%

model 2 Adjusted R square 5.506%

Hence model 2 is better.

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