Refining the model
sayedham
380_sta.docx
Description: From a pool of randomly queried Arizona State University Students, we observe if there is any correlation between number of credits hours enrolled in, amount of hours worked, distance traveled to school, and amount of caffeine consumption, with the average amount of hours a student sleeps on a school night. We believe that the time dedicated towards school, at an occupation, and traveling to school may decrease the amount of sleep; while caffeine consumption may occur to make up for lack of sufficient sleep.
|
n |
Sleep (hrs/night) |
Credit Hours |
Hours Worked Per Week |
Commute Distance (miles) |
Caffeine Consumption Per Week (items) |
n |
|
|
|
|
|
|
1 |
7 |
16 |
8 |
0 |
8 |
39 |
|
|
|
|
|
|
2 |
7 |
16 |
0 |
13 |
0 |
40 |
|
|
|
|
|
|
3 |
5 |
17 |
40 |
25 |
3 |
41 |
|
|
|
|
|
|
4 |
5 |
18 |
20 |
26 |
5 |
42 |
|
|
|
|
|
|
5 |
5 |
16 |
52 |
6 |
3 |
43 |
|
|
|
|
|
|
6 |
5 |
15 |
40 |
10 |
5 |
44 |
|
|
|
|
|
|
7 |
7 |
18 |
0 |
0 |
0 |
45 |
|
|
|
|
|
|
8 |
6 |
16 |
45 |
35 |
10 |
46 |
|
|
|
|
|
|
9 |
8 |
14 |
0 |
12 |
0 |
47 |
|
|
|
|
|
|
10 |
6 |
16 |
4 |
2 |
9 |
48 |
|
|
|
|
|
|
11 |
8 |
16 |
8 |
3 |
0 |
49 |
|
|
|
|
|
|
12 |
5 |
18 |
27 |
20 |
4 |
50 |
|
|
|
|
|
|
13 |
7.5 |
13 |
0 |
15 |
7 |
51 |
|
|
|
|
|
|
14 |
8 |
15 |
20 |
1 |
5 |
52 |
|
|
|
|
|
|
15 |
8 |
15 |
0 |
1.5 |
3 |
53 |
|
|
|
|
|
|
16 |
5 |
17 |
0 |
1 |
4 |
54 |
|
|
|
|
|
|
17 |
8 |
18 |
9 |
2 |
4 |
|
|
|
|
|
|
|
18 |
7 |
19 |
15 |
0 |
0 |
|
|
|
|
|
|
|
19 |
6 |
17.5 |
12 |
1.5 |
4 |
|
|
|
|
|
|
|
20 |
6 |
14 |
26 |
13 |
4 |
|
|
|
|
|
|
|
21 |
5 |
16 |
16 |
10 |
14 |
|
|
|
|
|
|
|
22 |
7 |
14 |
0 |
8 |
0 |
|
|
|
|
|
|
|
23 |
7 |
14 |
15 |
0.5 |
6 |
|
|
|
|
|
|
|
24 |
5.5 |
14 |
15 |
9 |
0 |
|
|
|
|
|
|
|
25 |
5 |
17 |
8 |
16 |
5 |
|
|
|
|
|
|
|
26 |
7 |
17 |
12 |
7 |
6.50 |
|
|
|
|
|
|
|
27 |
6 |
16 |
13 |
1 |
4 |
|
|
|
|
|
|
|
28 |
6 |
20 |
0 |
0.25 |
27.5 |
|
|
|
|
|
|
|
29 |
5 |
15 |
40 |
12 |
5 |
|
|
|
|
|
|
|
30 |
7 |
13 |
6 |
7.5 |
10 |
|
|
|
|
|
|
|
31 |
8 |
12 |
20 |
1 |
14 |
|
|
|
|
|
|
|
32 |
8 |
18 |
18 |
2 |
2 |
|
|
|
|
|
|
|
33 |
7 |
13 |
0 |
1 |
7 |
|
|
|
|
|
|
|
34 |
8 |
13 |
14 |
1.5 |
1 |
|
|
|
|
|
|
|
35 |
6 |
16 |
20 |
12 |
7 |
|
|
|
|
|
|
|
36 |
8 |
16 |
10 |
7 |
2 |
|
|
|
|
|
|
|
37 |
6 |
21 |
20 |
15 |
7 |
|
|
|
|
|
|
|
38 |
8 |
16 |
0 |
16 |
4 |
|
|
|
|
|
|
Here is the preliminary analysis generated from excel:
The same analysis was conducted in excel removing the data associated with the regressors that failed rejection (p > .10; credit hours and caffeine consumption):
Hypothesis:
Null Hypothesis: H0: β1 = β2 = β3 = β4 = 0
Alternative Hypothesis: H1: βj ≠ 0 for at least one j
[finish]
[refining the model]
Final Model:
where and are hours worked and commute distance in miles, respectively.
Discussion/Applicability:
The model
may be useful in predicting how much hours a student sleeps on a school night for future semesters and at different universities given how much hours they work and how far they travel to school. For the sake of education and in lieu of our relatively small sample size (n = 54, out of a student body comprised of tens of thousands of students) we elected to use an α value of 0.10. Thus, f0 > f0.10, 4, 49 (f0 = 4.21, computed from Excel’s ANOVA analysis; 2.04 < f0.10, 4, 49 < 2.09 according to the class provided F Distribution tables) the null hypothesis is rejected. Additional regression analysis was conducted on the regressors that were rejected (number of hours worked and commute distance to school in miles) and the final model indicates that there is a correlation between hours slept on a school night with the hours worked at a job and commute distance. An inverse relationship exists: as the number of hours worked and distance traveled to school increases, the amount of sleep on a school night decreases. Our data shows that there is no correlation between the number of credit hours a student is enrolled in and their weekly caffeine consumption.
SUMMARY OUTPUT
Regression Statistics
Multiple R0.505574
R Square0.255605
Adjusted R Square0.194838
Standard Error1.036428
Observations54
ANOVA
dfSSMSFSignificance F
Regression418.07344.5183494.2063150.005251
Residual4952.634941.074182
Total5370.70833
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept8.5543741.0515398.1350961.19E-106.44122710.667526.44122710.66752
Credit Hours-0.091140.063754-1.429550.159191-0.219260.036979-0.219260.036979
Hours Worked Per Week-0.022930.010338-2.217950.031225-0.0437-0.00215-0.0437-0.00215
Commute Distance (miles)-0.032510.014839-2.190730.033258-0.06233-0.00269-0.06233-0.00269
Caffeine Consumption Per Week (items)-0.03270.023559-1.388010.171414-0.080050.014644-0.080050.014644
SUMMARY OUTPUT
Regression Statistics
Multiple R0.43993949
R Square0.19354676
Adjusted R Square0.16192114
Standard Error1.05740122
Observations54
ANOVA
dfSSMSFSignificance F
Regression213.685376.8426846.1199360.004147338
Residual5157.022961.118097
Total5370.70833
CoefficientsS. Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept6.899882350.22272430.979569.59E-356.4527458177.3470196.452745827.3470189
Hours Worked Per Week-0.024771590.0105-2.359260.022179-0.045850721-0.003692-0.0458507-0.0036925
Commute Distance (miles)-0.026916770.014651-1.837210.072009-0.0563297340.002496-0.05632970.0024962
