This data has information about the price of various fast food items at an unspecified restaurant chain in different zip codes, along with various data on demographic and economic characteristics of the population in the zip code.
Regress the natural log of the price of soda on the proportion of the population that is black, the proportion of the population in poverty, the natural log of income, and the natural log of median housing value:
ln(price)= β_0+β_1 prop.black+ β_2 prop.povert+ β_3 ln(income)+ β_4 ln〖(house price)+u〗
Suppose you want to conduct a test that log income and the proportion of the population in poverty are jointly significant.
a) (10 points) Specify the null and alternative hypotheses.
b) (10 points) Write the specification of the restricted model.
c) (15 points) Calculate the F statistic for your test.
d) (15 points) Draw a conclusion regarding your hypothesis test (at the 5% significance level) by your preferred method.
2. For this question, use the data on sheet “Q2”.
Consider a standard “Mincer” type wage equation below
ln(wage)= β_0+β_1 educ+ β_2 exper+ β_3 tenure+u
a) (10 points) You want to test whether another year of general workforce experience (exper) has the same effect on wages as an additional year of tenure with the current employer (tenure). State the null and alternative hypothesis.
b) (10 points) Reparameterize your model in a way that Excel will be able to give you the appropriate standard errors. Show your reparameterized model.
c) (30 points) Test your null hypothesis from (2a) against a two sided alternative. What conclusion do you reach at the 5% significance level?
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