Test effect for linear regression

Question

Is there a way test if there is any overall effect by comparing a model with 1 predictor to a model with two predictors in R?

Answer 1

Yes, there are actually multiple measures for linear regression models. The quickest one to find and use, especially when you are only talking about the difference between one and two or three predictors, is the coefficient of determination. It is the proportion of the variance in the dependent variable that is predictable from the independent variable. The more of the variance in the response variable that is predicable, the better the model. Just use that as an indicator. Most statistical software will provide it as part of the linear model.

You might know it simply as R² _. The Chi² Goodness of fit tests can also be used as a secondary measure. Better fit, better model. Bear in mind, almost always, the more predictors the larger the R² This does not always mean that the extra predictors are better. If the difference in R² is small between two models, pick the simpler model.