Chapter 10.4, Problem 18BB

Confidence Intervals for a Regression Coefficients A confidence interval for the regression coefficient β₁is expressed as

b₁ − E < β₁ < b₁ + E

where

$E=t_{\alpha }/2^{s_b{}_{{}_1}}$

The critical t score is found using n − (k + 1) degrees of freedom, where k, n, and $s_b{}_{{}_1}$ are described in Exercise 17. Using the sample data from Example 1, n = 153 and k = 2, so df = 150 and the critical t scores are ±1.976 for a 95% confidence level. Use the sample data for Example 1, the Statdisk display in Example 1 on page 513, and the StatCrunch display in Exercise 17 to construct 95% confidence interval estimates of β₁ (the coefficient for the variable representing height) and β₂ (the coefficient for the variable representing waist circumference). Does either confidence interval include 0, suggesting that the variable be eliminated from the regression equation?