हिंदी

The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women. x y Mean 53 142 Variance 130 165 ∑(xi-x¯)(yi-y¯) = 1170

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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 women.

  x y
Mean 53 142
Variance 130 165

`sum(x_i - barx)(y_i - bary)` = 1170

योग
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उत्तर

Here. we need to find line of regressoin of y on x. which is given as:

`bary = "a" + "b"_("y"x)barx`

Where, byx = `("cov"("X", "Y"))/σ_x^2`

= `((sum(x_i - barx)(y_i - bary))/n)/(σ_x^2)`

= `(1170/10)/130` = 0.9

and a = `bary - barb_(yx)barx`

= 142 – (0.9)(53)

= 94.3

Therefore, regression equation of y on x is y = 94.3 + 0.9x

Now, the estimate of blood pressure of women with age 47 years is:

y = 94.3 + 0.9 × 4 7

= 136.6

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Properties of Regression Coefficients
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Regression coefficient of y on x = – 1.2

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