This problem uses an expanded version of the Boston Housing data. This version of the data contains five predictor variables for MEDV.

This problem uses an expanded version of the Boston Housing data. This version of the data contains five predictor variables for MEDV. The five variables are:

CRIM—crime rate per 1000 persons

NOX—nitric oxide concentration (parts per 10 million)

RM—average number of rooms per dwelling

PTRATIO—pupil–teacher ratio by town

LSTAT—% lower status of the population

(a) Make a scatterplot of MEDV versus CRIM. What do you see? On the basis of your scatterplot, does CRIM appear helpful in predicting MEDV?

(b) Run a regression of MEDV as a function of CRIM. Report a p-value and interpret it. From this, does CRIM appear helpful in predicting MEDV?

(c) Make a scatterplot of MEDV versus LSTAT. What do you see? On the basis of your scatterplot, does LSTAT appear helpful in predicting MEDV?

(d) Run a regression of MEDV as a function of LSTAT. Report a p-value and interpret it. From this, does LSTAT appear helpful in predicting MEDV?

(e) So far, we have been analyzing one predictor variable at a time so we do not have a good idea how they work together to affect MEDV. Run a multiple regression of MEDV versus all five of the predictor variables. Report the regression equation and the predictor variable p-values from the computer output. From this, does the regression appear helpful in predicting MEDV?

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