The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

Years of Schooling
Mean Wage, $
Number of People
6
4.4567
3
7
5.7700
5
8
5.9787
15
9
7.3317
12
10
7.3182
17
11
6.5844
27
12
7.8182
218
13
7.8351
37
14
11.0223
56
15
10.6738
13
16
10.8361
70
17
13.6150
24
18
13.5310
31
Total
528
18
16
14
12
10
8
6
4
6
8
10
12
14
Education
Mean wage
Mean value
FIGURE 2.6
Relationship between
mean wages and
education.
TABLE 2.6
Mean Hourly Wage
by Education
14
Ernst R. Berndt, 
The Practice of Econometrics: Classic and Contemporary,
Addison Wesley, Reading,
Mass., 1991. Incidentally, this is an excellent book that the reader may want to read to find out how
econometricians go about doing research.
Source: Arthur S.
Goldberger, 
Introductory
Econometrics,
Harvard
University Press, Cambridge,
Mass., 1998, Table 1.1, p. 5
(adapted).
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Chapter 2
Two-Variable Regression Analysis: Some Basic Ideas
47
EXAMPLE 2.2
Mathematics SAT
Scores by Family
Income
Table 2.10 in Exercise 2.17 provides data on mean SAT (Scholastic Aptitude Test) scores on
critical reading, mathematics, and writing for college-bound seniors based on 947,347
students taking the SAT examination in 2007. Plotting the mean mathematics scores on
mean family income, we obtain the picture in Figure 2.7.
Note:
Because of the open-ended income brackets for the first and last income
categories shown in Table 2.10, the lowest average family income is assumed to be
$5,000 and the highest average family income is assumed to be $150,000.
160,000
120,000
80,000
40,000
Average family income, $
0
440
460
480
Average math score 
560
540
520
500
FIGURE 2.7
Relationship between
mean mathematics
SAT scores and mean
family income.
As Figure 2.7 shows, the average mathematics score increases as average family
income increases. Since the number of students taking the SAT examination is quite
large, it probably represents the entire population of seniors taking the examination.
Therefore, the regression line sketched in Figure 2.7 probably represents the population
regression line.
There may be several reasons for the observed positive relationship between the two
variables. For example, one might argue that students with higher family income can
better afford private tutoring for the SAT examinations. In addition, students with higher
family income are more likely to have parents who are highly educated. It is also possible
that students with higher mathematics scores come from better schools. The reader can
provide other explanations for the observed positive relationship between the two
variables.
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