Apply Procedure 14.2 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the predictor variable

Procedure 14.2

Purpose To find a confidence interval for the slope, β₁, of the population regression line.

Assumptions The four assumptions for regression inferences

Step 1

For a confidence level of 1 — α, use to find t_a/2 with df = n — 2.

Step 2

The endpoints of the confidence interval for ß₁ are

Step 3

Interpret the confidence interval.

Refer to Exercise 14.60; 99%.

Exercise 14.60

We repeat the information. Presuming that the assumptions for regression inferences are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

Following are the size and price data for custom homes from Exercise 14.24. Use α = 0.01.

b = t/2. Se Sxx