Question 1: You are given the following data based on 10 pairs of observations on Y and X.

Σy_i = 1110 ΣX_i = 1680 ΣX_iY_i = 204,200

ΣX_i² = 315,400 ΣY_i² = 133,300

Assuming all the assumptions of CLRM are fulfilled, obtain

a. b₁ and b₂.

b. standard errors of these estimators.

c. r².

d. Establish 95% confidence intervals for B₁ and B₂.

e. On the basis of the confidence intervals established in (d), can you accept the hypothesis that B₂ = 0?

Question 2: Based on data for the United States for the period 1965 to 2006, the following regression results were obtained:

GNP_t = -995.5183 + 8.7503M_1t   r² = 0.9488

se = (        )           (0.3214)

t = (- 3.8258)         (         )

where GNP is the gross national product ($, in billions) and M₁ is the money supply ($, in billions).

Note: M₁ includes currency, demand deposits, traveler's checks, and other checkable deposits.

a. Fill in the blank parentheses.

b. The monetarists maintain that money supply has a significant positive impact on GNP. How would you test this hypothesis?

c. What is the meaning of the negative intercept?

d. Suppose M₁ for 2007 is $750 billion. What is the mean forecast value of GNP for that year?

Question 3:  Table 3-6 gives data on X (net profits after tax in U.S. manufacturing industries [$, in millions]) and Y (cash dividend paid quarterly in manufacturing industries [$, in millions]) for years 1974 to 1986.

a. What relationship, if any, do you expect between cash dividend and after-tax profits?

b. Plot the scattergram between Y and X.

c. Does the scattergram support your expectations in part (a)?

cl. If so, do an OLS regression of Y on X and obtain the usual statistics.

e. Establish a 99% confidence interval for the true slope and test the hypothesis that the true slope coefficient is zero; that is, there is no relationship between dividend and the after-tax profit.

CASH DIVIDEND (Y) AND AFTER-TAX PROFITS (X) IN

U.S. MANUFACTURING INDUSTRIES, 1974-1986