(c) In this sample, for households without a member having an advanced degree, their average expenditure on food away from home is $44.96 per person.
Exercise 2.13
(a) We estimate that each additional 1000 FTE students increase real total academic cost per student by $266, holding all else constant. The intercept suggests if there were no students the real total academic cost per student would be $14,656. This is meaningless in the pure sense because there are no universities with zero students. However, it is true that many of the costs of a university, related to research and the functioning of hospitals, etc., carry on and are “fixed costs” with respect to student population.
(b) . We predict the total cost per student at LSU in 2011 to be $21,403.
(c) The least squares residual for LSU is . The regression prediction is too high, an over-prediction of $687.70.
(d) The least squares regression passes through the point of the means, so that . The average ACA is $20,732.98 for these 141 universities.
Exercise 2.14
(a) The elasticity at a point on the fitted regression line is . We are given the estimate of the slope and the mean wage in the non-urban area. The fitted least squares line passes through the point of the means, so that . The elasticity at the means is then .
(b) We are given the mean level of EDUC. Therefore . The elasticity is then . The variance of the elasticity is . The standard error of the elasticity is then . The standard error of the estimated slope is 0.16, so the standard error of the elasticity is .
(c) For the urban area . Given EDUC = 12 the predicted wage is . Given EDUC = 16 the predicted wage is .
For the non-urban area, . Given EDUC = 12 the predicted wage is . Given EDUC = 16 the predicted wage is .
Exercise 2.15
(a) The EZ estimator can be written as
where
, , and k3 = k4 = ... = kN = 0
Thus, is a linear estimator.
(b) Taking expectations yields