Question

a. Upon reviewing the results of a multiple regression involving 30 observations on cross-sectional data the Econometric Society suspected that the variances of the error terms might be related to the predicted values of the dependent variable. Alarmed by the prospects they quickly ran a simple regression yielding the following results:

ei2 = 10.956 + 3.068?̂? R2 = 0.096
Using hypothesis testing, test at a 5% level to see if the variance of error terms is related to the predicted values of

the dependent variable. - State hypotheses, calculated and critical values for the test statistic, and conclusion.

b. Upon reviewing the results of a multiple regression involving 30 observations on time series data the Econometric Society suspected that the error terms might be related to each other. Alarmed by the prospects they quickly ran another regression yielding the following results:

yi = 1631.5 + 0.786x1i + 16.188x2i - 0.211x3i n=29
(41.7) (2.509) (2.131) (1.979); D.W. = 1.89

Do the hypothesis test at a 2% level to see if the econometric society should have been alarmed by the results. - State hypotheses, calculated and critical values for the test statistic, and conclusion.

c. Suppose that you wish to estimate the magnitude of the relationship between the rate of return on the 30 Dow Jones industrials and two economic factors, the rate of inflation and the rate of growth of real GNP. You postulate the following relationship:

yt =α+ß1x1t +ß2x2t +εi

where yt = the rate of return on the Dow Jones in period t x1t = the rate of inflation in period t
x2t = the rate of growth in real GNP in period t

What are the statistical consequences of estimating the relationship between these variables using the above regression equation when the true regression relationship is given by the following equation?

yt =α+ß1x1t +ß2x2t +ß3x3t +εi

Answer 1

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