On the last page of this file you will find the Excel output for a multiple line
ID: 3197300 • Letter: O
Question
On the last page of this file you will find the Excel output for a multiple linear regression model. The model was built in an attempt to better understand why students at area high schools perform differently on the state high school mathematics exam. The average test score for a class of students is what we are trying to predict. In our attempt to understand why these exam scores differ, we use 3 independent variables: a rating (0-100) for the quality of the math degree obtained by the instructor, the age of the instructor, and the salary (in thousands) of the instructor. You are to address the following questions based on the output. Worth 25 points total.
Estimate the average math score for a class of students whose instructor is 52 years old, earns $48,000, and got her degree in a math program rated 72.
What percentage of the variations in math scores can be explained by this model?
Conduct a test to determine if the model, taken as a whole, provided us with any significant explanation of the differences in math scores. That is, should the model be retained for further analysis?
Which of the independent variables appear to be significant to the model? Which appear to be insignificant? What leads you to these conclusions?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.597512233
R Square
0.357020869
Adjusted R Square
0.303439274
Standard Error
7.724526046
Observations
40
ANOVA
df
SS
MS
F
Significance F
Regression
3
1192.732105
397.5774
6.663125
0.001076925
Residual
36
2148.058895
59.6683
Total
39
3340.791
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Intercept
35.67761801
7.278849159
4.901547
2.03E-05
20.9154278
Math Degree
0.247481581
0.069845662
3.543263
0.001115
0.105828014
Age
0.244830604
0.185213036
1.321886
0.194545
-0.130798841
Income
0.133296712
0.152818937
0.872253
0.388851
-0.176634456
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.597512233
R Square
0.357020869
Adjusted R Square
0.303439274
Standard Error
7.724526046
Observations
40
ANOVA
df
SS
MS
F
Significance F
Regression
3
1192.732105
397.5774
6.663125
0.001076925
Residual
36
2148.058895
59.6683
Total
39
3340.791
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Intercept
35.67761801
7.278849159
4.901547
2.03E-05
20.9154278
Math Degree
0.247481581
0.069845662
3.543263
0.001115
0.105828014
Age
0.244830604
0.185213036
1.321886
0.194545
-0.130798841
Income
0.133296712
0.152818937
0.872253
0.388851
-0.176634456
Explanation / Answer
Solution:
average test score=35.67761801+0.247481581(math degree)+0.244830604(age)+
0.133296712(income)
the average math score for a class of students whose instructor is 52 years old, earns $48,000, and got her degree in a math program rated 72.
average math score=
35.67761801+0.247481581*(72)+0.244830604*(52)+0.133296712*(48000)
=6464.47
average maths core of class=6464.47
What percentage of the variations in math scores can be explained by this model?
R sq=
0.357020869*100
=35.7%
35.7% variation in math scores can be explained by this model
Solutionc:
Conduct a test to determine if the model, taken as a whole, provided us with any significant explanation of the differences in math scores. That is, should the model be retained for further analysis?
F=6.663125
Solutiond:
For Age and income variables
p>0.05
Age and income are not significant variables
Math degree is significant variable as p<0.05
0.133296712(income)
the average math score for a class of students whose instructor is 52 years old, earns $48,000, and got her degree in a math program rated 72.
average math score=
35.67761801+0.247481581*(72)+0.244830604*(52)+0.133296712*(48000)
=6464.47
average maths core of class=6464.47
What percentage of the variations in math scores can be explained by this model?
R sq=
0.357020869*100
=35.7%
35.7% variation in math scores can be explained by this model
Solutionc:
Conduct a test to determine if the model, taken as a whole, provided us with any significant explanation of the differences in math scores. That is, should the model be retained for further analysis?
F=6.663125
p=0.001076925 p<0.05 Model is significant model be retained for further analysis?Solutiond:
For Age and income variables
p>0.05
Age and income are not significant variables
Math degree is significant variable as p<0.05
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