1. Consider the following estimated models, for a data set with 23 observations:

**(model A)** Ln H = 4.607 + 2.914 ln GNP - 3.349 ln POP + 0.319 ln UNEMP - 1.313 ln INTRATE

(t-stats) (0.21) (1.23) (-0.44) (0.95) (-3.17) R^{2} = 0.479

**(model B)** Ln H = -4.759 + 1.873 ln GNP - 1.229 ln INTRATE

(t-stats) (-1.45) (3.79) (-3.96) R^{2} = 0.442

where H = total housing units started in thousands

GNP = Gross National Product in constant 1982 dollars in billions

POP = U.S. population in millions

UNEMP = Unemployment rate, in percentage, among all workers

INTRATE = New mortgage yields, in percentage

a. In model A test the joint hypothesis (at the 5 percent level) that the coefficients for ln GNP, ln POP, ln UNEMP , and ln INTRATE are all zero. What do you conclude from the test?

b. Test each regression coefficient in model A (except the constant term) for significance at the 5 percent level. Based on your results, would you recommend that some variables be omitted? If yes, what and why?

c. In model A, test the joint hypothesis that the coefficients for ln POP and ln UNEMP are zero. Based on your result would you recommend that these variables be omitted? Explain why or why not.

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