Question

1. What are the main 3 indicators that you should review to evaluate the fit of the multiple regression model?
2. How do you determine if you have the right variables in your model? Are there things you can do to be sure

Answer 1

First of all look at the value of R​​​​​​2​​​. It tells you How well model can predict the variability in the dependent Variable. Higher the value of R​​​​​​2 indicates that model is a good fit . It means values are close to regression line. It is relative measure . It doesn't tell you exactly How far points are lying away from regression line. R​​​​​​2​​​​​ Is 80% , it means independent variables can explain 80% of variance in dependent variable, remaining 20% might be due to some other factors.

Second measure of goodness of fit is standard Error ( s). It tells you how far on an average points are lying from regression line. Smaller the value of s it is considered as better fit. It is in units of dependent variable. Say S is 1.66 then it indicates that average distance between actual data and fitted data is 1.66 units of dependent Variable.

Next Indicator is P value of F statistic. Lower p value than level of significance means model is significant. In other words independent variables play important role in predicting dependent Variable. But this test will test all independent variables simultaneously. It will not tell if any Variable is insignificant which can be removed.

To determine if all Variables are significant or not look at p value of t test statistic for each independent variable. Say there are 5 independent variables then there will be 5 p values. Look for p value that is greater than level of significance, that particular Variable can be removed since it is insignificant.