Question

For the following data, find the regression equation for predicting Y from X

X	Y
1	2
4	7
3	5
2	1
5	8
3	7

1a.

Group of answer choices

a. Ŷ = -2X + 8

b. Ŷ =2X + 8

c. Ŷ =1.8X - 0.4

d. Ŷ =1.8X + 0.4

1b.

For the following scores, find the regression equation for predicting Y from X

X	Y
3	8
6	4
3	5
3	5
5	3

Answer 1

Solution:

1a)

Here , n = 6

	X	Y	XY	X^2	Y^2
	1	2	2	1	4
	4	7	28	16	49
	3	5	15	9	25
	2	1	2	4	1
	5	8	40	25	64
	3	7	21	9	49
Sum	18	30	108	64	192

Now ,

Slope of the regression line is

   b = 1.8

Now , y intercept of the line is

   a = -0.4

The equation of the regression line is

= bx + a

= 1.8X - 0.4

1b)

Here n = 5

	X	Y	XY	X^2	Y^2
	3	8	24	9	64
	6	4	24	36	16
	3	5	15	9	25
	3	5	15	9	25
	5	3	15	25	9
Sum	20	25	93	88	139

Now ,

Slope of the regression line is

   b = -0.875

Now , y intercept of the line is

   a = 8.5

The equation of the regression line is

= bX + a

= -0.875X + 8.5