Question

*This question has several parts*

Seven participants were asked about the average number of hours they spent watching TV per week and the average number of hours of sleep they had per week. Responses from the 7 participants are presented in the table below.

Participant	Average number of hours watching TV per week (X)	Average number of hours of sleep per week (Y)
A	12	38
B	30	45
C	23	42
D	5	64
E	10	43
F	14	46
G	0	54

You will use the information above for several of the following questions.

Calculate the Sum of Squares of X (SS_X) given the data above. (rounded to the nearest tenth)

631.7

425.1

791.3

230.9

338.0

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

Calculate the Sum of Squares of Y (SS_Y) given the data above. (rounded to the nearest tenth)

241.1

463.7

592.6

824.1

75.3

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

Calculate the Sum of Products of X and Y (SP_XY) given the data above. (rounded to the nearest tenth)

495.2

-362.9

-292.3

-512.4

687.2

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

Calculate the correlation coefficient (r) between the two variables given the data above. (rounded to the nearest hundredth)

-0.38

0.52

-0.63

0.87

-0.54

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

Based on the correlation coefficient (r) you calculated above, which of the following best describes strength and direction of the correlation between average number of hours of TV watching per week and average number of hours of sleep per week?

Moderately strong, positive

Very weak, positive

Moderately strong, negative

Very weak, negative

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

Calculate the slope (b) of the least squares regression equation given the data above. (rounded to the nearest hundredth)

-0.46

-0.23

1.42

3.67

-4.56

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

Calculate the y-intercept (a) of the least squares regression equation given the data above. (rounded to the nearest hundredth)

72.21

53.65

0.41

34.85

47.06

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

Which of the following represents the least squares regression equationgiven the data above?

ŷ = -0.46X + 53.65

ŷ = -0.23X + 72.21

ŷ = 1.42X + 34.85

ŷ = -4.56X + 47.06

ŷ = 3.67X + 0.41

Use the data above measuring the average number of hours spent watching TV per week and the average number of hours of sleep per week for 7 participants.

If someone spent an average of 18 hours watching TV per week, based on your regression equation above, what is the average number of hours of sleep we would predict they had per week? (rounded to the nearest hundredth)

45.32

28.07

57.68

29.56

74.51

Answer 1

1)

SSx =631.7143

2)

SSY =463.7

3) SP =-292.3

4) correlation coefficient (r) =-0.5400

5) Moderately strong, negative

6) slope (b) =-0.46

7) y-intercept =53.64

8) ŷ = -0.46X + 53.65

9) predicted value =45.32