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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

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

Grade:

1 Answers

Latika Leekha
askIITians Faculty 165 Points
5 years ago
Hello student,
(a) The expected age of husband when the wife’s age is 12 years:
While considering this, we shall have to consider three things:
The correlation coefficient is +0.8, so we haveb 12. (0.8) = 9.6
By rounding off we get it as 10.
But, this also spares 0.2 which is not in correlation, so we have 25(0.2) = 5.
Also, given that on an average husband is 3 years older, so finally we have 10+5+3 = 18.
(b) Similarly, in this case we have 0.8(33) with standard deviation (0.2)4.
This gives the average as 26.4 with standard deviation 0.8
So, it is roughly between 25 to 27.

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