Model1 :qualified=4.5 + 0.28571*weight:relate Call: lm(formula = qualified ~ wei

Question

Model1 :qualified=4.5 + 0.28571*weight:relate

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

Model2:qualified=4.51164 + 0.63836*weight + 0.59788*relate - 0.09788*weight: relate

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

Residuals:
   Min     1Q Median     3Q    Max
-3.65 -1.15 -0.15   0.85   2.85

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)    4.51164    1.01676   4.437 1.62e-05 ***
weight         0.63836    0.63416   1.007    0.316   
relate         0.59788    0.63888   0.936    0.351   
weight:relate -0.09788    0.39435 -0.248    0.804   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.298 on 172 degrees of freedom
Multiple R-squared: 0.06599,   Adjusted R-squared: 0.0497
F-statistic: 4.051 on 3 and 172 DF, p-value: 0.008192

in what way model 1 equivalent to model 2? in what way is it different? between these two models, which one is better and why?

Explanation / Answer

Both the models are linear multiple regression model. Both contains the interaction terms.

In the model 1 the interaction terms are significant while in the model 2 the interacton term is not significant.

Model 2 is better than tha model 1 since the Multiple R-squared: 0.06599 for Model 2 fits the model better than model 1. This indicates the improvement in the model 2 as compared to model 1 since the R-squared value is increased.

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