Problem 3E

Suppose you fit the multiple regression model

y = β0 + β1x1 + β2x2 + β3x3 + ε

to n = 30 data points and obtain the following result:

The estimated standard errors of are 1.86 and .29, respectively.

a. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠ 0. Use a = .05.

b. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠ 0. Use a = .05.

c. The null hypothesis H0: β2 = 0 is not rejected. In contrast, the null hypothesis H0: β3 = 0 is rejected. Explain how this can happen even though .

th Tuesday, March 28 • Example 2: Smokers Beliefs About Health Risks Physicians have expressed concern that a majority of smokers do not view themselves as being at increased risk of cancer. A group of physicians offered the results of a study of 735 current smokers selected at random from U.S. households with telephones. Of the 735 smokers surveyed, 44% indicated that they believed they have a higher than average risk of cancer. Do these data suggest that the true pro