Section 9.5: Multiple Linear Regression

1. Explain how a multiple linear regression model differs from a simple linear regression model.
2. Describe the assumptions made by a multiple linear regression model in terms of how the prediction of the response changes as a function of each predictor.
3. Interpret the coefficients \(b_{0}, b_{1}, \ldots, b_{p}\) of a multiple linear regression model \(\widehat{y} = b_{0} + b_{1}x_{1} + \ldots + b_{p} x_{p}\) in terms of how the prediction of the response changes per unit change in one of the predictors.
4. Given a multiple linear regression model, use it to predict the value of the response at specified values of the predictors.
5. Interpret Minitab’s output from Fit Regression Model… for a multiple linear regression, including:
   • where the coefficients are listed
   • what hypothesis tests the \(P\)-values reported by Minitab correspond to
   • where the multiple linear regression model is given
6. Interpret the standard error of prediction \(S\) in the context of a multiple linear regression model.