Question

The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.

	X	Y
Mean	50	140
Variance	150	165

and `sum (x_i - bar x)(y_i - bar y) = 1120`. Find the prediction of blood pressure of a man of age 40 years.

Answer 1

Given, X = Age, Y = Systolic blood pressure,

n = 10, `bar x = 50","  bar y = 140`,

`sigma_X^2 = 150,  sigma_Y^2 = 165` and

`sum (x_i - bar x)(y_i - bar y) = 1120`

Since Var(X) = `(sum (x_i - bar x)^2)/n`,

`sigma_x^2 = (sum (x_i - bar x)^2)/n`

∴ `150 = (sum (x_i - bar x)^2)/10`

∴ `sum (x_i - bar x)^2 = 1500`

Now, `b_(YX) = (sum (x_i - bar x)(y_i - bar y))/(sum (x_i - bar x)^2) = 1120/1500 = 0.7`

∴ The regression equation of systolic blood pressure of the men (Y) on their age (X) is 

`(Y - bar y) = b_(YX) (X - bar x)`

∴ (Y − 140) = 0.7(X − 50)

∴ Y − 140 = 0.7X − 35

∴ Y = 0.7X − 35 + 140

∴ Y = 0.7X + 105

For X = 40,

Y = 0.7(40) + 105

Y = 28 + 105

Y = 133

∴ The man of age 40 years has a systolic blood pressure of 133.