A college instructor is interested in the relationship between number of class m
ID: 3370032 • Letter: A
Question
A college instructor is interested in the relationship between number of class missed by SIUE students during the semester and their final exam score. He collected data from a SRS of 40 students. The following outputs are given
Formula = final score - clas missed
Estimate
Standard Error
intercept
87.292
4.816
Class missed
-2.981
0.440
Multiple R squared ; 0.548
Answer the following questions
What is the prediction equation?
What is the value of the slope? Interpret the slope in the context of the question.
Construct a 95% CI for B1. Based on the confidence interval, can we conclude that number of class missed has relationship with the final exam score? Explain.
Suppose for a student who missed 5 classes, what is the expected final score?
Complete the following ANOVA table
Source Regression
SS
df
MS
F
Error
229
Total
19266
39
In R output, it can be seen that r^2 = 0.548. Interpret what the number means. And calculate what is the correlation between number of class missed and final exam score.
Estimate
Standard Error
intercept
87.292
4.816
Class missed
-2.981
0.440
Explanation / Answer
Ans:
1)
a)Regression equation:
Perdicted final score=-2.981*class missed+87.292
slope=-2.981
Interpretation of slope:For each class missed,there will be decrease in final exam score on average of 2.981
critical t value=tinv(0.05,38)=2.024
95% confidence interval for B1
=-2.981+/-2.024*0.440
=-2.981+/-0.891
=(-3.872,-2.090),yes , we conclude that number of class missed has relationship with the final exam score.
(as,0 is not included in the above confidence interval)
When number of missed classes=5
Perdicted final score=-2.981*5+87.292=72.387
2)
R^2=0.548,it indicates that 54.8% of the variation in final exam score is explained by the number of classes missed.
Cofficient of correlation=sqrt(0.548)=0.74
Source SS df MS F Regression 10564 1 10564 46.13 Error 8702 38 229 Total 19266 39Related Questions
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