Question

Returns on common stocks in the United States and overseas appear to be growing more closely correlated as economies become more interdependent. Suppose that the following population regression line connects the total annual returns (in percent) on two indexes of stock prices:

MEAN OVERSEAS RETURN = −0.07 + 0.20 ✕ U.S. RETURN

(a) What is β₀ in this line?

β₀ is the population slope, −0.07.β₀ is the population slope, 0.20.     β₀ is the population intercept, −0.07.β₀ is the population intercept, 0.20.

What does this number say about overseas returns when the U.S. market is flat (0% return)?

This says that the mean overseas return is  % when the U.S. return is 0%.

(b) What is β₁ in this line?

β₁ is the population slope, −0.07.β₁ is the population slope, 0.20.     β₁ is the population intercept, −0.07.β₁ is the population intercept, 0.20.

What does this number say about the relationship between U.S. and overseas returns?

This says that when the U.S. return changes by 1%, the mean overseas return changes by  %.

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We know that overseas returns will vary in years when U.S. returns do not vary. Write the regression model based on the population regression line given above.

y_i = _______ +_________ x_i + ε_i, where y_i and x_i

are observed overseas and U.S. returns in a given year, and ε_i are independent

N(0, σ)

variables.

What part of this model allows overseas returns to vary when U.S. returns remain the same?

( ) σ_i

( ) x_i

( ) y_i

( ) ε_i

Answer 1

(a) β₀ is the population intercept, −0.07.

This says that the mean overseas return is -0.07% when the U.S. return is 0%.

(b) β₁ is the population slope, 0.20.

This says that when the U.S. return changes by 1%, the mean overseas return changes by 0.20%.

c) We know that overseas returns will vary in years when U.S. returns do not vary. Write the regression model based on the population regression line given above.

y_i = -0.07 + 0.20 x_i + ε_i

Part of this model allows overseas returns to vary when U.S. returns remain the same = ε_i