Chapter 14.3, Problem 12AYU

(a)

To determine

To construct: Correlation matrix between $x_1,x_2,x_3,x_4\text{and}y$.

To determine

To find: Whether multicollinearity is a problem or not.

(b)

To determine

Multiple regression line.

To determine

To test: The provided hypothesis.

To determine

The explanatory variables that have slope coefficients that are not significantly different from zero.

(c)

To determine

Multiple regression line when a variable with the maximum p-value ($x_2$) gets removed from the model.

To determine

To test: Whether the model obtained in part (c) above is significant or not.

To determine

Multiple regression line when any additional variable with the maximum p-value has been removed from the model.

(d)

To determine

To draw: Residual plots.

To determine

To draw: Boxplot of the residuals.

(e)

To determine

To predict: Value of $y$ using the final model constructed in part (c).

(f)

To determine

To draw: Normal probability plot of the residuals.

To determine

To explain: Whether confidence interval and prediction interval should be constructed or not.

(g)

To determine

95% prediction and confidence intervals.