MGCR 271: Business Statistics
Midterm Exam, 26 Oct 2012
12:00 PM - 2:00 PM
Grading Guide
Student Name McGill ID
Please circle the name of your instructor.
Instructor P. Dantoni D. Hart R.Vaidyanathan G. Zabowski
INSTRUCTIONS
1. Please write your NAME and STUDENT NUMBER on the exam paper.
2. This examination is PRINTED ON BOTH SIDES of the paper.
3. This examination consists of a total of 5 QUESTIONS for 50 POINTS.
4. This examination consists of 14 pages plus 8 pages of tables.
5. If you nd any pages MISSING, bring it to the attention of the invigilator immediately.
6. SPACE IS PROVIDED on the examination to answer all questions.
7. MARKS allotted to each question appear next to question numbers.
8. This is a CLOSED BOOK examination and counts for 20% of your nal grade.
9. TABLES are provided and SELECTED FORMULAE are on the last page of the examination.
10. Show LOGIC since part marks will be given for method and partial results.
11. If you feel that a question is ambiguous, briey explain your interpretation or assumptions.
12. You are permitted TRANSLATION dictionaries ONLY.
13. You are permitted a STANDARD CALCULATOR ONLY.
14. This examination and the tables provided MUST BE RETURNED.
For Use by Graders Only
Question 1 2 3 4 5 Total
Score
1 1. (10 points) A researcher was investigating variables that might be associated with the academic
performance of high school students. He examined data from 1994-1995 for each of the 50 states
plus the District of Columbia. The data included the following variables.
expend Average expenditure per student (in thousands of US dollars)
ratio Average pupil/teacher ratio
salary Estimated average annual salary of teachers (in thousands of US dollars)
frac Percentage of all eligible students taking the SAT
verbal Average verbal SAT score
math Average math SAT score
sat Average total SAT score
In particular, the researcher is interested in how teacher salaries are related with SAT scores. Shown
below is a scatterplot of the data and a summary of the regression results.
1100
1000
sat
900
25 30 35 40 45 50
salary
Coefcient Std. Error t value Pr>j j)
(Intercept) 1158.85 57.65 20.10 0.0000
salary -5.53 1.63 -3.39 0.0014
2 In addition, he also calculated the correlation between all the variables, as shown below.
expend ratio salary frac verbal math sat
expend 1.0000 -0.371025 0.869802 0.5926 -0.41005 -0.34941 -0.38054
ratio -0.3710 1.000000 -0.001146 -0.2131 0.06377 0.09542 0.08125
salary 0.8698 -0.001146 1.000000 0.6168 -0.47696 -0.40131 -0.43988
frac 0.5926 -0.213054 0.616780 1.0000 -0.89326 -0.86938 -0.88712
verbal -0.4100 0.063767 -0.476964 -0.8933 1.00000 0.97026 0.99150
math -0.3494 0.095422 -0.401313 -0.8694 0.97026 1.00000 0.99350
sat -0.3805 0.081254 -0.439883 -0.8871 0.99150 0.99350 1.00000
(a) (2 points) Interpret the scatterplot in the context of the relationship being explored. Do you
see anything surprising about the relationship?
(1 point) The relationship betweensalary and sat scores isweakly linear and negative.
(1 point) This is surprising since we would expect to see a positive relationship, with
higher sat scores in states where the teachers are paid a higher salary.
(b) (2 points) The state of Wisconsin decides to increase the annual salary of its teachers by 5000
dollars. How would the average SAT scores for students in this state change?
(1 point) The slope of the regression line is -5.53, and it represents the increase in sat
score associated with a $1,000 increase in salary.
(1 point) Hence, a $5,000 increase in salary will change the average SAT score for students
in Wisconsin by5.53 5 = 27.65
(c) (2 points) What percentage of the variation in math SAT scores is explained by the average
expenditure per student?
(1 point) The correlation between math SAT scores and average expenditure per student
is0.3494.
(1 point) Hence, the percentage of variation in math SAT scores explained by average
2
expenditure per student ( 0.3494) = 0.1221, which equals 12.208%.
(d) (2 points) Between expenditure per student, average salary paid and pupil/teacher ratio,
which of these variables best explains verbal SAT scores. Explain your answer
(1 point) The correlation between verbal SAT scores and the x variables given are -0.41,
-0.4769 and 0.0637 respectively.
(1 point) Since percentage of variation explained by a variable is the square of its correla-
tion, average salary paid best explains verbal SAT s(r= 0.4769).
3
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