(35) Suppose you are doing a study on household milk consumption, and using a sample of n = 33 households you obtained a regression line of: y =...

2. (35) Suppose you are doing a study on household milk consumption, and using a sample of n = 33 households you obtained a regression line of:

yˆ = .012 (.005) + .088x1 (.079) + 1.76x2 (.792) + −1.62x3 (.56)

where the numbers in parentheses represent the standard error of the coefficient estimates. Furthermore, each variable is:

y = Milk consumption in quarts per week

x1 = weekly income, in hundreds of dollars

x2 = family size

x3 = a dummy variable that equals 1 if one of the members of the family is lactose intolerant, and 0 otherwise

(a) (7) What would you predict would be the household milk consumption for a family with 4 members, a weekly income of $1, 500, and with a lactose-intolerant family member?

(b) (7) Test the null hypothesis β1 = 0 against the two-sided alternative at the α = .05 significance level using the t distribution. Page 2

(c) (7) Test the null hypothesis β2 = 0 against the two-sided alternative at the α = .05 significance level using the t distribution

(d) (7) Construct a 95% confidence interval for β3.

(e) (7) The 99% confidence interval for β1 is (−.1297, .3057).

The 99% confidence interval for β2 is (−.423, 3.94).

The 99% confidence interval for β3 is (−3.16, −.0767)

Without doing the hypothesis test, answer the following: for which of these βi would you reject the null H0 : βi = 0 against the two-sided alternative at the α = .01 significance level? 

3.(16) You are conducting a study and obtained the following regression equation:

yˆ = 75 + 470.2x1 − 12032.11x2 + .11111x3

n = 17

SST = 1, 000

SSE = 375

Test the null hypothesis βi = 0 for i = 1, 2, 3 against the alternative that at least one βi 6= 0 at the α = .01 significance level.