5. Imagine you are interested in studying the relationship between climate and i
ID: 1103156 • Letter: 5
Question
5. Imagine you are interested in studying the relationship between climate and income across U.S. cities. You run the following model: log (GDP) = 0 + ,Temp + 2 Precip + u Where log(GDP) is the city's Gross Domestic Product per capita in thousands of dollars, Temp is the average city's temperature in degrees Celsius, and Precip is the average annual precipitation in centimeters log(GDP)= 10.51-0.011 Temp+ 0.0003 Precip 0.0239) 0001) R2= 0.014, n=79 a. How many degrees of freedom does this model have? b.Test the null hypothesis that temp has no effect on log(GDP) against the alternative that it does, at the 5% level of significance. write down all steps including what the null and alternative hypotheses are. Test the null hypothesis that precip has no effect on log(GDP) against the alternative that is has a positive effect, at the 5% level of significance. Write down all steps including what the null and alternative hypotheses are. c.Explanation / Answer
a. This model has 77 degrees of freedom. This is as there are 79 observations and there are 2 regressors, thus the model has 79-2=77 degrees of freedom.
b. Here we will use a t test and so the null hypothesis is H0:B2=0,H1:B2 not equal to 0. Thus we have the t stat in this case t = -0.011/0.0239 = 0.46. This is the B1 coefficient divided by the standard error. Thus we accept the null hypothesis at the 5% level of significance that temp has no effect on log(GDP).
c. Here we will use a t test and so the null hypothesis is H0:B2=0,H1:B2 not equal to 0. Thus we have the t stat in this case t = 0.0003/0.0001 = 3. This is the B2 coefficient divided by the standard error. Thus we reject the null hypothesis at the 5% level of significance that precip has no effect on log(GDP). Precip does have an effect on log GDP.
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