# Question

A market researcher is interested in the average amount of money spent per year by college students on clothing. From 25 years of annual data, the following estimated regression was obtained through least squares:

where

y = expenditure per student, in dollars, on clothes

x1 = disposable income per student, in dollars, after the payment of tuition, fees, and room and board

x2 = index of advertising, aimed at the student market, on clothes

The numbers in parentheses below the coefficients are the coefficient standard errors.

a. Test, at the 5% level against the obvious one-sided alternative, the null hypothesis that, all else being equal, advertising does not affect expenditures on clothes in this market.

b. Find a 95% confidence interval for the coefficient on x1 in the population regression.

c. With advertising held fixed, what would be the expected impact over time of a $1 increase in disposable income per student on clothing expenditure?

where

y = expenditure per student, in dollars, on clothes

x1 = disposable income per student, in dollars, after the payment of tuition, fees, and room and board

x2 = index of advertising, aimed at the student market, on clothes

The numbers in parentheses below the coefficients are the coefficient standard errors.

a. Test, at the 5% level against the obvious one-sided alternative, the null hypothesis that, all else being equal, advertising does not affect expenditures on clothes in this market.

b. Find a 95% confidence interval for the coefficient on x1 in the population regression.

c. With advertising held fixed, what would be the expected impact over time of a $1 increase in disposable income per student on clothing expenditure?

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