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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.
Solution
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 equaiton 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 = 28 + 105 = 133
∴ The man of age 40 years has systolic blood pressure 133.
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