# The age in years of 7 young couples is given below. Calculate husband’s age when wife’s age is 38 years. Husband (x) 21 25 26 24 22 30 20 Wife (y) 19 20 24 20 22 24 18 - Mathematics and Statistics

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The age in years of 7 young couples is given below. Calculate husband’s age when wife’s age is 38 years.

 Husband (x) 21 25 26 24 22 30 20 Wife (y) 19 20 24 20 22 24 18

#### Solution

Given, X = Age of husband,

Y = Age of wife

 X = xi Y = yi xi2 yi2 xiyi 21 19 441 361 399 25 20 625 400 500 26 24 676 576 624 24 20 576 400 480 22 22 484 484 484 30 24 900 576 720 20 18 400 324 360 Total 168 147 4102 3121 3567

From the table, we have

n = 7, sumx_"i" = 168,  sumy_"i" = 147, sumx_"i"^2 = 4102

sumx_"i"y_"i" = 3567, sumy"i"^2 = 3121

∴ bar(x) = (sumx_"i")/"n" = 168/7 = 24

bar(y) = (sumy_"i")/"n" = 147/7 = 21

byx = (sumx_"i"y_"i" - "n"bar(x) bar(y))/(sumx_"i"^2 - "n"bar(x)^2)

= (3567 - 7 xx 24 xx 21)/(4102 - 7 xx (24)^2

= (3567 - 3528)/(4102 - 4032)

= 39/70

= 0.557

Now, a = bar(y) - "b"_(yx)  bar(x)

= 21 – 0.557 × 24

= 21 – 13.368

= 7.632

bxy = (sumx_"i"y_"i" - "n"bar(x) bar(y))/(sumy_"i"^2 - "n"bar(y)^2)

= (3567 - 7 xx 24 xx 21)/(4102 - 7 xx (21)^2

= (3567 - 3528)/(3121 - 3087)

= 39/34

= 1.147

Now, a' = bar(x) - "b"_(xy)  bar(y)

= 24 – 1.147 × 21

= 24 – 24.087

= – 0.087

The regression equation of age of husband (X) on age of wife (Y) is

X = a' + bxy Y

∴ X = – 0.087 + 1.147 Y

when wife’s age is 38 years, Y = 38

∴ X = – 0.087 + 1.147 × 38 = 43.5

∴ Husband’s age is 43.5 years, when wife’s age is 38 years.

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Chapter 2.3: Linear Regression - Q.4

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