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Final Exam 2007 - MATH 423

# Final Exam 2007 - MATH 423 - MATH 423 Final Examination...

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MATH 423 Final Examination December 18, 2007 Student Name: Student Number: McGill University Faculty of Science FINAL EXAMINATION MATH 423 Regression and Analysis of Variance December 18th, 2007 9 a.m. - 12 Noon Calculators are allowed. One 8.5” × 11” two-sided sheet of notes is allowed. Language dictionaries are allowed. You must do BOTH of the first two questions (Questions 1 and 2) and TWO of the remaining THREE questions (Questions 3 through 5) . You will receive points from the two questions with the highest marks from Questions 3, 4, and 5. Question 6 is worth 10 bonus points. You will not lose points on the exam for any work on this question, you can only add points for any correct work that you provide. There are 12 pages to this exam. The total number of marks for the exam is 100, although it is possible score as high as 110 due to the bonus question. Examiner: Professor Russell Steele Associate Examiner: Professor David Stephens 1

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MATH 423 Final Examination December 18, 2007 Question 1: (30 points) Average public teacher pay and spending on public schools per pupil in 1985 for 50 states and the District of Columbia were reported by the Albuquerque Tribune. Output from regression analyses are reported at the end of the exam and questions about the analysis of the data are below. The variables in the data set are: PAY: Average public school teacher annual salary (in \$) SPEND: Spending on public schools per pupil (in \$) AR: Region corresponding to East , Central , and West The primary research question of interest is to determine the extent to which the spending per pupil and area are associated with the average public school teacher salary. Refer to the code and output at the end of the test for the following questions. (a) Test for significance of both covariates individually (not in the presence of the other). Refer clearly to the part(s) of the output that you are using for your tests. (b) Give an interpretation for each of the coefficient estimates in model4 . (c) Test for a statistically significant interaction between area and spending for modelling teacher pay. Refer clearly to the part(s) of the output that you are using for your tests. (d) Comment on the appropriateness of the model assumptions and the stability of model4 . Should the researcher have any concerns about the validity of inferences made from this model? Why or why not?
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