Question

You are given the following data
X Y
Mean 36 85
SD 11 8
R=0.66, find out (a) two regression line, (b) value of x when y=75

Answer 1

Answer:

(a) The two regression line are:

     $Line1:y-0.48x=67.72\\Line2:x-0.9075y=-41.1375$

(b) The value of x for y = 75 is:

     $Line 1: x=3.4944\\Line 2:x=26.925$

Step-by-step explanation:

The equation of regression line of Y on X is:

$(y-\bar y) = r\frac{\sigma_{y}}{\sigma_{x}} (x-\bar x)$

And the equation of regression line of X on Y is:

$(x-\bar x) = r\frac{\sigma_{x}}{\sigma_{y}} (y-\bar y)$

Given:

$\bar x=36\\\bar y=85\\\sigma_{x}=11\\\sigma_{y}=8\\r=0.66$

(a)

The regression line of Y on X is:

$(y-\bar y) = r\frac{\sigma_{y}}{\sigma_{x}} (x-\bar x)\\(y-85)=0.66\times\frac{8}{11}\times (x-36)\\ y-85=0.48x-17.28\\y-0.48x=67.72$

The regression line of X on Y is:

$(x-\bar x) = r\frac{\sigma_{x}}{\sigma_{y}} (y-\bar y)\\(x-36)=0.66\times\frac{11}{8}\times (y-85)\\ x-36=0.9075y-77.1375\\x-0.9075y=-41.1375$

Thus, the two regression line are:

$y-0.48x=67.72\\x-0.9075y=-41.1375$

(b)

The value of x when the value of y is 75 is:

• Using the regression line $y-0.48x=67.72$

          $y-0.48x=67.72\\75-0.48x=67.72\\0.48x=7.28\\x=3.4944$

• Using the regression line $x-0.9075y=-41.1375$

          $x-0.9075y=-41.1375\\x-(0.9075\times75)=-41.1375\\x=26.925$

Thus, the value of x is 3.4944 and 26.925 using the two regression lines respectively.

Learn More: https://brainly.in/question/8932658

Answer 2

Step-by-step explanation:

I don't no understand this math please explain simple process