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Calculate the least squares

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Question :1. Consider an industry consisting of 25 firms, each producing y from input x.

The observed data are:

where y=log(output) and x=log(labor hours), and 'log' stands for the natural logarithm.

A) Calculate the Least Squares (LS) estimates of α and β for the linear model.

B) Test the hypothesis β^ =2.8.

C) Form a 99% CI for σ2 - the variance of ε.

2. Data from a different time period of the same industry are used to obtain the following
i iii
estimated regression y^ =20+0.5x, R2 =0.2; y =35; x =11;n=10; Σi(xi -x‾) =86

Test the hypothesis that the slopes in this year and previous period (Question 1 above) are the same (assuming the variances of the disturbances are the same). Assume the disturbances in both problems are the same, so the two models can be pooled to estimate a common σ2 [Hint: manipulate the previous results to determine the joint/pooled moments.]

3. You have learned in one of your economics courses that one of the determinants of per capita income (the "Wealth of Nations") is the population growth rate. Furthermore you also found out that the Penn World Tables contain income and population data for 104 countries of the world. To test this theory, you regress the GDP per worker (relative to the United States) in 1990 (RelPersInc) on the difference between the average population growth rate of that country (n) to the U.S. average population growth rate (nus ) for the years 1980 to 1990. This results in the following regression output:

RelPersInc= 0.518-18.831x(n - nus),R2 =0.522,SER= 0.197

a) Interpret the results carefully.

b) Is this relationship economically important?

c) What would happen to the slope, intercept, and regression R2 if you ran another regression where the above explanatory variable was replaced by n only, i.e., the average population growth rate of the country? (The population growth rate of the United States from 1980 to 1990 was 0.009.) Should this have any affect on the t-statistic of the slope?

d) 31 of the 104 countries have a dependent variable of less than 0.10. Does it therefore make sense to interpret the intercept?

Attachment:- linear model.rar

Reference no: EM132398480

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