There is often thought to be a relationship between a person’s educational attai
ID: 2955751 • Letter: T
Question
There is often thought to be a relationship between a person’s educational attainment and the number of children he or she has. The hypothesis is that as one’s educational level increases, he or she has fewer children. Investigate this conjecture with 25 cases drawn from the 2006 GSS file. The following table displays educational attainment, in years, and the number of children for each respondent.
Education
Children
Education
Children
16
0
12
2
12
1
12
3
12
3
11
1
6
6
12
2
14
2
11
2
14
2
12
0
16
2
12
2
12
2
12
3
17
2
12
4
12
3
12
1
14
4
14
0
13
0
12
3
12
1
Education
Children
Education
Children
16
0
12
2
12
1
12
3
12
3
11
1
6
6
12
2
14
2
11
2
14
2
12
0
16
2
12
2
12
2
12
3
17
2
12
4
12
3
12
1
14
4
14
0
13
0
12
3
12
1
Explanation / Answer
In the regression equation Y= ax +b you can get a using the formula r * sy/sx where sy is the standard deviation of y and sx is the standard deviation of x. Doing that you get a= -.046995* 1.428286/2.083267= -0.3222. B equals the mean of y less a times the mean of x. This is 2.04- (-0.3222)* 12.56= 6.087. So the regression equation is Y= -0.3222 x +6.087. If you put x=16 in this equation, you get 0.93 for y or 1 child. This of course is an approximation, not an exact number, but it is still useful. If you square r you get .221, which is called the coefficient of determination. It tells you that 22% of the change in Y can be explained by the change in x, and the rest by outside factors.Related Questions
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