Chapter 10.4, Problem 17BB

Testing Hypotheses About Regression Coefficients If the coefficient β₁, has a nonzero value, then it is helpful in predicting the value of the response variable. If β₁  = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that β₁ = 0 use the test statistic t = (b₁ − 0)/ ${\text{s}}_{{\text{b}}_1}$. Critical values or P-values can be found using the t distribution with n − (k + 1) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error ${\text{s}}_{{\text{b}}_1}$ is often provided by software. For example, see the accompanying StatCrunch display for Example 1, which shows that ${\text{s}}_{{\text{b}}_1}$ = 0.071141412 (found in the column with the heading of "Std. Err.” and the row corresponding to the first predictor variable of height). Use the sample data in Data Set 1 “Body Data” and the StatCrunch display to test the claim that β₁ = 0. Also test the claim that β₂ = 0. What do the results imply about the regression equation?