If the coefficient β1 has a non-zero 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)/sb1. 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 sb1 is often provided by software. For example, the Minitab display in Example 1 shows that sb1 = 0.1289. Use the sample data in Table 10-4 and the Minitab display in Example 1 to test the claim that β1 = 0. Also test the claim that β2 = 0. What do the results imply about the regression equation?

Table 10-4 Heights (in inches) of Mothers, Fathers, and Their Daughters Height of Mother Height of Father 64 65 67 72 72 72 Height of Daughter 58.6 64.7 65.3 61.0 65.4 67.4 60.9 63.1 60.0 71.1 62.2 67.2 63.4 68.4 62 2 64.7 59.6 61.0 64.0 65.4 67 64 65 67 59 72 75 67 70 69 69 69 64