Question

2.
Calculate the regression equations of X on
Y and Y on X from the following data:
X
10
12
13
17
18
Y
5
6
7
9
13​

Answer 1

Explanation:

XY Regression Mo▋

Burhanuddin Nadiadi

Calculate the regression equations of X on

Y and Y on X from the following data:

X

10

12

13

17

18

Y

5

6

7

9

13

To calculate the regression equation of X on Y, we need to find the slope and intercept of the regression line using the formula:

b = r(sx/sy)

a = y̅ - bx̅

where r is the correlation coefficient, sx is the standard deviation of X, sy is the standard deviation of Y, x̅ is the mean of X, y̅ is the mean of Y, b is the slope, and a is the intercept.

To calculate the regression equation of Y on X, we need to use the same formula but with Y and X switched.

First, we need to calculate some values:

X: 10 12 13 17 18

Y: 5 6 7 9 13

x̅ = (10+12+13+17+18)/5 = 14

y̅ = (5+6+7+9+13)/5 = 8

sx = sqrt(((10-14)^2 + (12-14)^2 + (13-14)^2 + (17-14)^2 + (18-14)^2)/4) = 3.162

sy = sqrt(((5-8)^2 + (6-8)^2 + (7-8)^2 + (9-8)^2 + (13-8)^2)/4) = 2.588

r = Σ((Xi - x̅)(Yi - y̅)) / sqrt(Σ(Xi - x̅)^2 * Σ(Yi - y̅)^2)

r = ((10-14)(5-8) + (12-14)(6-8) + (13-14)(7-8) + (17-14)(9-8) + (18-14)*(13-8)) / sqrt(((10-14)^2 + (12-14)^2 + (13-14)^2 + (17-14)^2 + (18-14)^2) * ((5-8)^2 + (6-8)^2 + (7-8)^2 + (9-8)^2 + (13-8)^2))

r = 0.892

Now we can calculate the regression equation of X on Y:

b = r(sx/sy) = 0.892(3.162/2.588) = 1.090

a = y̅ - bx̅ = 8 - 1.090(14) = -4.06

Therefore, the regression equation of X on Y is:

X = -4.06 + 1.090Y

To calculate the regression equation of Y on X:

b = r(sy/sx) = 0.892(2.588/3.162) = 0.732

a = y̅ - bx̅ = 8 - 0.732(14) = -1.85

Therefore, the regression equation of Y on X is:

Y = -1.85 + 0.732X