# Question: A stockbroker is interested in the factors influencing the rate

A stockbroker is interested in the factors influencing the rate of return on the common stock of banks. For a sample of 30 banks, the following regression was estimated by least squares:

where

y = percentage rate of return on common stock of bank

x1 = percentage rate of growth of bank’s earnings

x2 = percentage rate of growth of bank’s assets

x3 = loan losses as percentage of bank’s assets

x4 = 1 if bank head office is in New York City and 0 otherwise

The numbers below the coefficients are the coefficient standard errors.

a. Interpret the estimated coefficient on x4.

b. Interpret the coefficient of determination, and use it to test the null hypothesis that, taken as a group, the four independent variables do not linearly influence the dependent variable.

c. Let ei denote the residuals from the fitted regression and y`i the in-sample predicted values of the dependent variable. The least squares regression of e`i on y`i yielded coefficient of determination 0.082. What can be concluded from this finding?

where

y = percentage rate of return on common stock of bank

x1 = percentage rate of growth of bank’s earnings

x2 = percentage rate of growth of bank’s assets

x3 = loan losses as percentage of bank’s assets

x4 = 1 if bank head office is in New York City and 0 otherwise

The numbers below the coefficients are the coefficient standard errors.

a. Interpret the estimated coefficient on x4.

b. Interpret the coefficient of determination, and use it to test the null hypothesis that, taken as a group, the four independent variables do not linearly influence the dependent variable.

c. Let ei denote the residuals from the fitted regression and y`i the in-sample predicted values of the dependent variable. The least squares regression of e`i on y`i yielded coefficient of determination 0.082. What can be concluded from this finding?

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