STA Class #2: Multiple Linear Regression

• The relationship between X1 and Y may change when we control (aka, add to the model) another predictor —> X2

• R-squared will always increase when you add more variables

• When testing individual coefficients for multiple linear regression, if 0 is not in the confidence interval, that tells us that the variable has a statistically significant relationship with Y after holding all other X variables constant

RSE:

• Interpretation: When using the model to make a prediction, we expect the model to be off by ± the RSE value, on average

• We expect 95% of predicted values to be between ± (2 x the RSE value) of the actual values

• Like with simple regression, the residual standard error is approximately equal to the standard deviation of the residuals

R-Squared

• Interpretation: Multiple R-squared value % of the variablility in the y-variable can be explained by the predictors in the model

• SQRT(R-squared) = R, which is the correlation between y-hat and y