Exercise 2.5
(a) The consultant’s report implies that the least squares estimates satisfy the following two equations
Solving these two equations yields
Therefore, the estimated regression used by the consultant is:
Figure xr2.5 Fitted regression line and mean
Exercise 2.6
(a) The intercept estimate is an estimate of the number of sodas sold when the temperature is 0 degrees Fahrenheit. A common problem when interpreting the estimated intercept is that we often do not have any data points near . If we have no observations in the region where temperature is 0, then the estimated relationship may not be a good approximation to reality in that region. Clearly, it is impossible to sell -240 sodas and so this estimate should not be accepted as a sensible one.
The slope estimate is an estimate of the increase in sodas sold when temperature increases by 1 Fahrenheit degree. This estimate does make sense. One would expect the number of sodas sold to increase as temperature increases.
(b) If temperature is 80°F, the predicted number of sodas sold is
(c) If no sodas are sold, and
or
Thus, she predicts no sodas will be sold below 12°F.
(d) A graph of the estimated regression line:
Figure xr2.6 Fitted regression line
Exercise 2.7
(a) Since
it follows that
(b) The standard error for is
Also,
Thus,