business travelers probably would have more incentive than the typical
respondent to express their true preferences about air travel. The airline
also could test different types of business-class seating (at different fares)
on various flights. Obviously, the company must extend the test long
enough and publicize it adequately so that business travelers will have
time to make up their minds about the new options. Although
information from the actual test may be more accurate than that gleaned
from surveys, it is also likely to be much more expensive.- The most direct way is to estimate the equation
where Y 1 denotes last quarter’s income. For instance, the relevant data
for the second quarter of year 1 is Q 33.6, P 265, P250, and Y 1
104 (i.e., first quarter’s income).- Reducing the number of data points typically worsens the quality of the
estimated regression equation. R^2 may decrease or increase. (By luck, the
remaining points may or may not lie more nearly along a straight line.)
The reduction in observations tends to produce a reduction in the
adjusted R-squared. Using only the odd-numbered quarters, R^2 falls to .72
and adjusted R-squared is .65. - With fewer data points for estimation, one would expect the F-statistic to
fall (because of fewer degrees of freedom), the coefficient estimates to
change, and their standard errors to increase. The regression output
based on odd-numbered quarters confirms this: F 3.43. Since the
critical F-value (3 and 4 degrees of freedom) is 6.59, the equation lacks
overall explanatory power at the 95 percent confidence level. The
estimated equation is
The respective standard errors are 19.4, .72, .76, and 1.9. Applying a t-test
shows that Pand Y are not significantly different than zero. With so little
data, it is impossible to detect the real effects of these two variables.
Finally, the standard error of the regression increases to 19.4.- The value of Company A’s stock after 35 years will be PA50(1.05)^35
$275.8. (We can find this value by direct calculation or by using a future-
value table found in most finance textbooks). In turn, the value of
Company B’s stock will be PB50(1.06)^35 $384.3. The lesson is that
small differences in average growth rates (when compounded over long
periods of time) can lead to very large differences in value. - The utility has not erred in using only a single dummy. By setting W 0,
the utility obtains the summer equation, Qt80.5 2.6t. By setting W 1,
it has the winter equation, Qt(80.5 12.4) 2.6t 92.9 2.6t. Thus,
Q71.72.81P.74P3.5Y.
QabPcPdY 1 ,180 Chapter 4 Estimating and Forecasting Demandc04EstimatingandForecastingDemand.qxd 9/5/11 5:49 PM Page 180