3. Anja Stoll is a chemistry professor at a large public university in the Midwe

Question

3. Anja Stoll is a chemistry professor at a large public university in the Midwest. She kept track of the class attendance of her students and the homework results of each of her students. The variable class reflects the number of lectures a student attended. Professor Stoll taught 24 lectures. The variable homework reflects the score in a homework assignment with a maximum of 100 points. After the midterm with a maximum score of 100 points Ms Stoll estimates the following regression model. Midterm,-¿ +/,class, + B,homework, +5 The resulting excel output is: R Square Standard Error ANOVA MS 5015.72507.9 1785.9 101.1 72 17.81 1.41 6.43 0.12 2.77 0.0071 11.48 0.0000 0003 class a) Joe attended all classes and received 85 points on the homework. Frank attended 18 classes and received 73 points on his homework. What are the predicted midterm scores of Joe and Frank? what is our estimate for the coefficient ?? Using plain English, explain the meaning of this estimate. Is this estimate equal to ?. smaller than ?, or larger than ?? b) c) Calculate the 90% confidence interval for the effect of class attendance on the midterm results- holding homework grades fixed. d) If we conducted a t-test to see if the homework score affects the midterm results, would we be able to reject the null that there is no effect of the homework results on midterm with 95% certainty? Explain your answer e) What is the estimated the variance of the error term u?

Explanation / Answer

Please see the answers as shown below: -

a)

Joe:

Scores=17.81+1.41*24+0.47*85=91.6

Frank:

Scores=17.81+1.41*18+0.47*73=77.5

b)

Estimate of class is 1.41 which means that for every increase of 1 in class, scores would go up by 1.41 keeping everything else constant

c)

tCRIT is 1.666

1.41-1.666*0.12=1.21

1.41+1.666*0.12=1.61

d)

p-value is 0.0003 which means we can reject the null hypothesis.

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