Answer to Question #6382 in Statistics and Probability for Rashmi Gupta

Question

5. The ages of husbands and wives in a community were found to have a correlation coefficient equal to +0.8; the average of husbands’ ages was 25 years and that of wives’ ages 22 years; their standard deviations were respectively 4 and 5 years. Find the two lines of regression and from the lines ,measure
a. The expected age of husband when wife’s age is 12 years
b. The expected age of wife when husband’s age is 33 years

Answer 1

The ages of husbands and wives in a community were found to have a correlation coefficient equal to +0.8; the average of husbands’ ages was 25 years and that of wives’ ages 22 years; their standard deviations were respectively 4 and 5 years. Find the two lines of regression and from the lines ,measure
a. The expected age of husband when wife’s age is 12 years
The answer has three factors in it.
1) Since there is 0.8 correlation coefficient, this gives 12*0.8 = 9.6; rounds to 10;
2) This leaves 0.2 that is not in correlation, and that gives 25*0.2 = 5; and
3) On the average, the husband is 3 years older.
Altogether this gives 10 + 5 + 3 = 18.
b. The age of 33 for a wife puts the husband at 0.8(33) with a standard deviaton of 0.2(4).
That is, the husband is, on the average, 26.4, with a st dev of 0.8.
That puts the husband age rougly as at least 25 and at most 27.