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प्रश्न
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.
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उत्तर
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.
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