Lecture Questions
A few questions for you: In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.5; both averaged 12 years of schooling completed, with a SD of 3 years
Note: Associated with an increase of one SD in x, there is an increase of only r.SD’s in y, on the average. Plotting these regressions estimates give the regression line for y on x.
(a) Predict the educational level of a woman whose husband has completed 18 years of schooling.
(b) Predict the educational level of a man whose wife has completed 15 years of schooling.
(c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible?
Solution:
Given Xbar = Ybar = 12, slope, m = 0.5
SD = 3
We can calculate the y-intercept, given the mean values of x and y, using the formula
y = mx + c
Solving for c, we get
c = y -mx
= 12 - .5 *12 = 6
Using c=6, and m= 0.5, we can now predict
a. The educational level of a woman whose husband has completed 18 years of schooling.
Let x be number of years of schooling the husband has completed. Therefore we can predict the education level, y, of the wife as
y = mx + c
= .5(18) + 6 = 15 years
b. The educational level of a husband whose wife has completed 15 years of schooling.
Let x denotes the number of years that schooling the wife has completed. Therefore we can predict the education level, y, of the husband as y = mx + c
= .5(15) + 6 = 13.5 years
c. If all the data were available, we could see in the scatter diagram that, the variation around the least square lines is very high, thus giving this conflicting results.