Exercise 2.22 (continued)
(c) The estimated equations using a sample of regular classes and regular classes with a full-time teacher aide (when SMALL = 0) are given in Table xr2-22b
Table xr2-22b
CAIDENSSE
TOTALSCORECoeff916.44174.30658374356550
Std. err.(3.5586)(4.9940)
READSCORECoeff432.66502.8714837733335
Std. err.(1.4600)(2.0489)
MATHSCORECoeff483.77671.43518371907234
Std. err.(2.3546)(3.3043)
Students in regular classes without a teacher aide achieve an average total score of 916.4 while students in regular classes with a teacher aide achieve an average total score of 920.7. This is an increase of 0.47%. These results suggest that having a full-time teacher aide has a small impact on learning outcomes as measured by totals of all achievement test scores.
(d) The estimated equations using a sample of regular classes and regular classes with a full-time teacher aide are
The effect of having a teacher aide on learning is 0.66% for reading and 0.30% for math. These increases are smaller than the increases provided by smaller classes.
Exercise 2.23
(a)
Figure xr2.23(a) Vote against Growth
There appears to be a positive association between VOTE and GROWTH.
(b) The estimated equation for 1916 to 2012 is
The coefficient 0.9639 suggests that for a 1 percentage point increase in a favorable growth rate of GDP in the 3 quarters before the election there is an estimated increase in the share of votes of the democratic party of 0.9639 percentage points.
We estimate, based on the fitted regression intercept, that that the Democratic party’s expected vote is 48.62% when the growth rate in GDP is zero. This suggests that when there is no real GDP growth, the Democratic party is expected to lose the popular vote. A graph of the fitted line and data is shown in the following figure.
Figure xr2.23(a) Vote vs Growth fitted
Exercise 2.23 (continued)
(c) In 2016 the actual growth rate in GDP was 0.97% and the predicted expected vote in favor of the Democratic party was , or 49.55%. The actual popular vote in favor of the Democratic party was 50.82%.
(d) The figure below shows a plot of VOTE against INFLATION. It is difficult to see if there is positive or inverse relationship.
Figure xr2.23(d) Vote against Inflat
(e) The estimated equation (plotted in the figure below) is
We estimate that a 1 percentage point increase in inflation during the party’s first 15 quarters increases the share of Democratic party’s vote by 0.2616 percentage points. The estimated intercept suggests that when inflation is at 0% for that party’s first 15 quarters, the expected share of votes won by the Democratic party is 49.6%.
Figure xr2.23(e) Vote vs Inflat fitted
Exercise 2.23 (continued)
(f) The actual inflation value in the 2016 election was 1.42%. The predicted vote in favor of the Democratic candidate (Clinton) was , or 49.99%.
Exercise 2.24
(a) The histogram shows a very skewed distribution
Figure xr2.24(a) Histogram of real hammer price
The sample mean, based on 422 works that sold is $78,682. But the 25th, 50th and 75th percentiles are $2,125, $13,408 and $46,102 respectively; all less than the mean which is inflated due to some extreme values. The two largest values are $3,559,910 and $3,560,247.