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Interpret the following regression equation together with all the supporting statistics where Yt is the number of new cars sold (millions of units), X1t is the disposable income of consumers ($B), X2t is the price of a new car (an index number where 1982-84=100), and X3t is the 5-year Treasury Bond rate (%). The values reported in parenthesis directly below the regression coefficients are the t-calculated values for the respective coefficients.
Fcal = 25.98
R2 = .58
Yt=.002 + .005X1t - .025X2t - .125X3t n=28 (1956-84)
(4.12) (5.23) (-1.51) (-2.65)
Assume that the model was re-estimated in its double logarithmic form and the results read:
Fcal = 30.28
R2 = .62
lnYt=.002 + 1.4 5lnX1t - .75lnX2t - 1.10lnX3t n=28
(3.12) (4.33) (-2.21) (-1.65)
Interpret this model and relate to the concept of elasticity. Write the model in its exponential format with the relevant coefficients.
Overheard at water cooler: My regression model of demand is better than one that the consultant prepared for us because it has a higher R2.
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Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 123034.4703 23311.13897 5.277926165 0.000358709 71094.01589 174974.9248 71094.01589 174974.9248 y 0.238078372 0.017797354 13.37717818 1.04516E-07 0.19842..
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