Question

1. Use this scenario to answer questions 45-50. In cases where rounding is required, round to three decimal places.

   Suppose you are interested in estimating the number of hours a person exercises (y-variable) from their age (x-variable). The following data is collected.

   x	18	26	32	38	52	59
   y	10	7	4	5	2	1

   Calculate r.

4 points   

QUESTION 46

1. Based on r, is linear regression justified in this case?

   Yes

   No

4 points   

QUESTION 47

1. Calculate  (the slope of the regression equation).

4 points   

QUESTION 48

1. Calculate  (the y-intercept of the regression equation).

4 points   

QUESTION 49

1. Assuming that this is a useful model, predict the hours a person exercises if they are 36 years old.

4 points   

QUESTION 50

1. Calculate the residual value for the observation (x = 32, y = 4)

Answer 1

Ans:

	x	y	xy	x^2	y^2
1	18	10	180	324	100
2	26	7	182	676	49
3	32	4	128	1024	16
4	38	5	190	1444	25
5	52	2	104	2704	4
6	59	1	59	3481	1
Total	225	29	843	9653	195

1)

r=(6*843-225*29)/SQRT((6*9653-225^2)*(6*195-29^2))

r=-0.947

2)Yes

3)

slope,b=(6*843-225*29)/(6*9653-225^2)=-0.201

4)

y-intercept,a=(29-(-0.20115)*225)/6=12.377

5)

regression equation:

y'=12.377-0.201x

when x=36

y'=12.377-0.201*36=5.141

6)

when x=32

y'=12.377-0.201*32=5.945

Residual=4-5.945=-1.945