Question

given that means of x and y 65 and 67 standard deviation and coefficient of correlation difference between than is 8 draw regression lines​

Answer 1

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Answer 2

The equation of  y on x  is given as y = 1.12x - 5.8.

Given:

The mean of x and y is 65 and 67 respectively.

The standard deviation of x and y is 2.5 and 3.5 respectively.

The coefficient of correlation is given to be 0.8

To Find:

Regression of Y on X.

Solution:

We have been given that

Mean of x, $\bar{X}$  = 65

Mean of y, $\bar{Y}$ = 67

The standard deviation of x, $\sigma_{x}$ = 2.5

The standard deviation of y, $\sigma_{y}$ = 3.5

Coefficient of correlation of x and y, r(x, y) = 0.8

The equation of regression of y on x is given as:

$\frac{ y -\bar{Y} }{\sigma_{y} }$ = $r_{xy}$ $\frac{x-\bar{X} }{\sigma_{x} }$

Substituting the given values of mean, standard deviation, and coefficient of correlation, we have

$\frac{y-67}{3.5}$ = 0.8 × $\frac{x-65}{2.5}$

⇒ y - 67 = 1.12 (x - 65)

⇒ y = 1.12x - 72.8 + 67

⇒ y = 1.12x - 5.8

∴ The equation of  y on x  is given as y = 1.12x - 5.8.

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