1. A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of tree using the height (in feet) and diameter (in inches) of the trees. The height and diameter of 31 trees of a certain species were measured, the trees were cut down, and the volume of usable lumber was determined. The multiple linear regression model
Volume = 0 + 1(Diameter) + 2(Height) + i
is assumed to hold, where the deviations i are independent and Normally distributed with mean 0 and standard deviation . This model is fit to the data using the method of least squares and an estimate of 2 is found to be s2 = 15.07. The degrees of freedom for this estimate are
A. 28.
B. 29.
C. 30.
2. An old saying in golf is "you drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money. To explore the relation between winning, putting, and driving distance, data on the top 69 money winners on the PGA tour in 1993 are used. The average number of putts per hole for each player and their average driving distance is used to predict their total winnings using the multiple regression model
where the deviations εI are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software.
Based on these results, a 95% confidence interval for β2 is
A. -5341854. ± 3031678.
B. 18491.3 ± 4060.
C. 18491.3 ± 8120.