# Question

The following regression was fitted by least squares to 30 annual observations on time-series data:

where

yt = number of business failures

x1t = rate of unemployment

x2t = short-term interest rate

x3t = value of new business orders placed The numbers below the coefficients are the coefficient standard errors.

a. Interpret the estimated coefficient on log x3t in the context of the assumed model.

b. What null hypothesis can be tested by the d statistic? Carry out this test for the present problem using a 1% significance level.

c. Given your results in part b, is it possible to test, with the information given, the null hypothesis that, all else being equal, short-term interest rates do not influence business failures?

d. Estimate the correlation between adjacent error terms in the regression model.

where

yt = number of business failures

x1t = rate of unemployment

x2t = short-term interest rate

x3t = value of new business orders placed The numbers below the coefficients are the coefficient standard errors.

a. Interpret the estimated coefficient on log x3t in the context of the assumed model.

b. What null hypothesis can be tested by the d statistic? Carry out this test for the present problem using a 1% significance level.

c. Given your results in part b, is it possible to test, with the information given, the null hypothesis that, all else being equal, short-term interest rates do not influence business failures?

d. Estimate the correlation between adjacent error terms in the regression model.

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