Question

We are interested in predicting lung function using demographic characteristics. We fitted 3 multiple linear regression models to our data.

Model 1 with an explanatory variable of sex had an R2 of 0.87 and an adjusted R2 of 0.86.

Model 2 including smoking status and height had an R2 of 0.95 and an adjusted R2 of 0.81.

Model 3 including sex, smoking status, and height had an R2 of 0.95 and an adjusted R2 of 0.75.

Without other information, which model seems to be the best choice, balancing model fit with the size of the model?

i.) Model 3

ii.) Model 2

iii.) Model 2 and Model 3 are equally good choices

iv.) Model 1

I understand the model with higher adjusted R2 is the best model. I think answer is one of the models M1 or M2 (ii or iv). However, I am not sure which one is the best model and how?

Please respond only if you are 100% confident about the answer and provide a reasoning why you think that's the answer. Thank you.

Answer 1

If you are testing best goodness of fit to a set of Linear regression on multiple variable, it is always suggested that you use Adjusted R-squared to compare the models. Always remember that greater adj(R square) is better

So it is clear that Adj(R square) of Model 1 is greatest among the the all three models. So best choice should be Model 1

Ans : iv) Model 1