(b)
Figure xr2.25(e) Observations and log-linear fitted line
The residuals do not appear randomly distributed. There is a “spray” pattern with a concentration of observations along the lower edge.
(c)
We estimate that the expected per person expenditure for households with no advanced degree holder is $42.76. We estimate that the expected per person expenditure for households with an advanced degree holder is $73.15, which is $30.39 higher.
(d) The sample means for the two groups are shown below. The mean of the observations with ADVANCED = 0 is the estimated intercept in (c), and the estimated mean of the observations with ADVANCED = 1 is $30.39 higher, the estimated coefficient of advanced in part (c).
NMean
ADVANCED = 125773.15494
ADVANCED = 094342.76161
Exercise 2.27
(a)
Figure xr2.27(a) Motel_pct vs. 100relprice
There seems to be an inverse association between relative price and occupancy rate.
(b)
Based economic reasoning we anticipate a negative coefficient for RELPRICE. The slope estimate is interpreted as saying, the expected model occupancy rate falls by 1.22% given a 1% increase in relative price, other factors held constant.
Exercise 2.27 (continued)
(c)
Figure xr2.27(c) OLS residuals
The residuals are scattered about zero for the first 16 observations but for observations 17-23 all but one of the residuals is negative. This suggests that the occupancy rate was lower than predicted by the regression model for these dates. Randomly scattered time series residuals should not have strings of consecutive observations with the same sign.
(d)
We estimate that during the non-repair period the expected occupancy rate is 79.35%. During the repair period, the expected occupancy rate is estimated to fall by 13.24%, other things held constant, to 66.11%.
Exercise 2.28
(a)
variableNmeanmedianminmaxskewnesskurtosis
WAGE120023.6419.33.94221.12.959427.5787
Figure xr2.28(a1) Histogram and statistics for WAGE
The observations for WAGE are skewed to the right indicating that most of the observations lie between the hourly wages of 5 to 50, and that there is a smaller proportion of observations with an hourly wage greater than 50. Half of the sample earns an hourly wage of more than $19.30 per hour, with the average being $23.64 per hour. The maximum earned in this sample is $221.10 per hour and the least earned in this sample is $3.94 per hour.
variableNmeanmedianminmaxskewnesskurtosis
EDUC120014.2014021−.456254.95745
Figure xr2.28(a2) Histogram and statistics for EDUC
307 people had 12 years of education, implying that they finished their education at the end of high school. There are a few observations at less than 12, representing those who did not complete high school. The spike at 16 years describes those 304 who completed a 4-year college degree, while those at 18 and 21 years represent a master’s degree, and further education such as a PhD, respectively. Spikes at 13 and 14 years are people who had one or two years at college.
Exercise 2.28 (continued)
(b) The estimated model is
The coefficient 2.3968 represents the estimated increase in the expected hourly wage rate for an extra year of education. The coefficient −10.4 represents the estimated wage rate of a worker with no years of education. It should not be considered meaningful as it is not possible to have a negative hourly wage rate.