Question

The following data are from a random sample of 10 students who participated in a study...

The following data are from a random sample of 10 students who participated in a study undertaken to investigate the effect of sleep time (measured in average number of hours of sleep per night) on GPA (grade point average, measured on a 4-point scale).

Student

Sleep time

GPA

1

7

3.28

2

9

3.16

3

8

3.75

4

6

2.50

5

4

2.45

6

8

2.91

7

7

3.53

8

6

3.02

9

3

2.30

10

8

3.48

a. Find the equation between GPA (y) as function of sleep time (x).

b. What is the estimated GPA of a student who averages 5 hours of sleep per night?

c. What is the coefficient of determination?

Math   Statistics-And-Probability   
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Answer #1

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.77235
R Square 0.596524
Adjusted R Square 0.546089
Standard Error 0.334186
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 1.320919 1.320919 11.82769 0.008835
Residual 8 0.893441 0.11168
Total 9 2.21436
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 1.70537 0.401641 4.246003 0.002814 0.779184 2.631557
sleep time 0.201914 0.05871 3.439141 0.008835 0.066527 0.3373

a. the equation between GPA (y) as function of sleep time (x) is

y =1.70537+0.201914 *x

b. the estimated GPA of a student who averages 5 hours of sleep per night is

y =1.70537+0.201914 *5 = 2.715

c. the coefficient of determination is 0.5965

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