5. Does studying really pay off? To answer that question, a curious student in a
ID: 3244460 • Letter: 5
Question
5. Does studying really pay off? To answer that question, a curious student in a statistics class asked 10 students how many hours they studied for the most recent test and the grade they received. The data are recorded here. GRADE 89 92 32 92 90 30 87 88 34 30 HOURS 25 26 12 32 29 10 21 27 15 18 a. Estimate a linear regression equation using Data Analysis in Excel. (10 pts) b. Based upon the coefficient of the regression model, what do you conclude? (4 pts) c. If you study one more hour, on average, what will happen to your grade according to the model? (5 pts) 5. continued d. Using a GLOBAL test, is there evidence of a linear relationship between the number of hours spent studying and a student’s grade on the test? Use alpha =0.01. (15pts)
Explanation / Answer
Let,
X = Hours
Y = Grade
Y
X
89
25
92
26
32
12
92
32
90
29
30
10
87
21
88
27
34
15
30
18
Now we go to excel. We type the data in excel. We select the tab Data. There we can find Data Analysis. Under Data Analysis we find Regression. We click Regression, we select X and Y data and finally click on OK. We get the summary output as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.902
R Square
0.813
Adjusted R Square
0.789
Standard Error
13.812
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
6626.306022
6626.306022
34.736
0.0004
Residual
8
1526.093978
190.7617473
Total
9
8152.4
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 99.0%
Upper 99.0%
Intercept
-11.365
13.8986
-0.8177
0.4372
-43.4154
20.6853
-58.0004
35.2703
X Variable 1
3.617
0.6137
5.8937
0.0004
2.2018
5.0322
1.5578
5.6762
Question a)
The line of regression,
y^ = -11.365 +3.617x
Question b)
We get the value of intercept as -11.365. This is the value of the grade when a student studied 0 hours.
We get the value of the slope as 3.617. We can conclude that if there is one hour increment in the part of the variable Hours then the variable grade is going to be increased by 3.617 unit.
Question c)
If I read one more hours than my grade will be increased by 3.617 unit.
Question d)
H0: There is no linear relationship
H1: There is a significant linear relationship
Level of significance is .01
Test Statistics:
F = 34.736
p-value = .0004
p-value < .01 (level of significance)
We reject the null hypothesis at 1% level of significance.
There is evidence of a linear relationship between the number of hours spent studying and student’s grade on the test.
Y
X
89
25
92
26
32
12
92
32
90
29
30
10
87
21
88
27
34
15
30
18
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