Answers to the Regression examples at the end of Lecture 5
Answers to the Regression examples at the end of Lecture 5
Example #1: Suppose you conduct a regression with n=9 data points, and generate the following results:
Qi= 10 - .5Pi + .1 Ai
(5) (.03) (.2)
n = 9, R2 = .83 Adj. R2 = .773, F2,6 = 14.6 (p =.003)
a. Interpret R2, and adjusted R2
R2 = .83 implies that 83% of the variation in data from average sales is explained by the regression.
Adjusted R2 =.773 implies that 77.3% of the variation in data from average sales is explained by the regression, after controlling for the potential loss in explanatory power caused by adding additional independent variables.
b. Does the regression explain movement in Q better than the simple average of Q?
The F2,7 =14.6 (p = .003). The F test statistic indicates (roughly) that the regression equation explains 14.6 times more of the variation in the data than it leaves unexplained. The p = .003 indicates that 99.7% percent of the time a regression that explained no more of the movement in the data than the simple average of sales would explain as much as this estimate.
c. Can we conclude that price has an independent effect in explaining the movement in sales, Qi?
A ( 2 std. error range about the estimate, -.44 to -.56 excludes zero. Thus we may conclude at a 95% confidence level that price decreases increases sales quantities.
Example #2. Consider a regression with the log of data.
lnQi= 50 - .2 ln Pi + .12ln Ai F2,9 =9.56 (p=.0001)
(20) (.3) (.08)
n = 12, R2 = .68, Adj R2 = .64
a. Interpret R2, and adjusted R2
See answer to 1 a. above
b. Does the regression explain movement in Q better than the simple average of Q?
The F2,10 =9.56 (p = .0001). The F test statistic indicates (roughly) that the regression equation explains 9.56 times more of the variation in the data than it leaves unexplained. The p = .0001 indicates that 99.99% percent of the time a regression that explained no more of the movement in the data than the simple average of sales would explain as much as this estimate.
c. Can we conclude that price alone explains movement in sales, Qi?
A ( 2 std. error range about the estimate, -.8 to +.4 includes zero. Thus we may not conclude at a 95% confidence level that price decreases increases sales quantities.
Notice finally, that we can make one further interesting insight with a log linear regression. Observe that (=-.3 Notice that two standard deviations about -.3 are not necessarily greater than zero. However, this interval does not include -1. Thus, we can conclude that we are on the inelastic portion of the demand curve.
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