# QMB 3200 Homework #12 (Sample Exam #3)

Subject: Mathematics / Statistics
Question
QMB 3200

Homework #12 (Sample Exam #3)
Max. Score: 65 points

Duration: 2 Hours (You should be able to solve these problems within 2 Hours)
Instructions:
1. You must answer all Problems and Questions. Maximum score possible for this Homework is 65 points.
2. Presenting only the final answer is not sufficient to get complete credit. Show the steps in solution approach. That way partial credit can be earned to various steps in final solution. It is your responsibility to demonstrate mastery of the subject matter through your answers.
3. Submit your report as an Excel file. Solve each problem on a separate tab (worksheet). No Exceptions.Organize your solutions on the Excel worksheet properly. Show where your answers are for each problem and the sections of the problem. Use Proper formatting
4. Name Your File to show your Full Name and the HW Number
6. Do not wait until the last minute.The deadline is strictly enforced by Canvas. No hardcopy submissions are accepted. No e-mail submissions are accepted.If your file does not appear on Canvas by the deadline, zero points will be recorded for you for that HW. No exceptions are entertained for any reason under any circumstance in this regard.
1. [33 points] The U.S. Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and trucks. A portion of the sample data for 311 compact, midsize, and large cars follows. The column labeled Class identifies the size of the car; Compact, Midsize, or Large. The column labeled Displacement shows the engine’s displacement in liters. The column labeled Fuel Type shows whether the car uses premium (P) or regular (R) fuel, and the column labeled Hwy MPG shows the fuel efficiency rating for highway driving in terms of miles per gallon. A partial report of regression analysis is provided below. Answer the questions based on the report.

Regression Analysis: Hwy MPG versus Displacement, ClassMidsize, …
Predictor

Coef

SE Coef

T

P

Constant

29.7624

0.5521

53.91

0.000

Displacement

-1.6347

0.1169

-13.98

0.000

ClassMidsize

3.9634

0.3193

0.000

ClassLarge

1.6450

0.2940

0.000

-1.1210

0.2090

0.000

S = 1.64596 R-Sq = 83.4% R-Sq(adj) = 83.2%

Analysis of Variance
Source

DF

SS

MS

F

P

Regression

0.000

Residual Error

829.0

Total

4989.3

Predicted Values for New Observations

New Obs Fit SE Fit 99% CI 99% PI

1 25.3822 0.2233 (24.8033, 25.9610) (21.0767, 29.6876)

Values of Predictors for New Observations

New Obs Displacement ClassMidsize ClassLarge FuelPremium

1 3.00 0.000000 1.00 1.00

a) What is the sample size used for the analysis? (1 point)

b) What type of variables are “Class” and “Fuel Type”? Show how they are represented in the regression analysis. (3 points)

c) Identify the Dependent Variable and the Independent Variables in the model. (1 point)

d) Calculate ‘t’ test statistic values. Complete the ANOVA Table. (3 points)

e) Write down Hypothesis Statements. Conduct both p-value and critical-value based hypothesis tests at 0.01 level of significance. Is the Multiple Regression between “Hwy MPG”, Car “Class”, Engine “Displacement”, and “Fuel Type” statistically significant? (4 points)

f) Write down Hypothesis Statements. Which ones among the independent variables are statistically significant at 0.01 level of significance? How are you able to determine the same? (3 points)

g) Write down the estimated regression equation in terms of the dependent and independent variables for the given problem (Use variable names – Do not use y, x … etc.). (2 points)

h) Interpret the coefficient for the variable “Displacement”. (2 points)

i) What are the values of Multiple Coefficient of Determination and Adjusted Multiple Coefficient of Determination? (2 points)

j) Verify Why R-Sq and R-Sq (adj) values are equal to 83.4% and 83.2% respectively. (2 points)

k) What is the interpretation of R-Sq = 83.4%? (2 points)

l) Would you recommend using the estimated regression equation? What is your basis? (2 points)

m) What is the expected Hwy MPG for “Compact” cars with “Displacement” = 1.6 Liters when “Regular Fuel” is used? (2 points)

n) What is the expected Hwy MPG for: “Large” cars with “Engine Displacement” = 3.0 Liters when “Premium Fuel” is used (which is the new observation in the report above)? (2 points)

o) What is the 99% interval estimate on “mean” Hwy MPG for “Large” cars with “Engine Displacement” = 3.0 Liters when “Premium Fuel” is used (which is the new observation in the report above)? (2 points)

2. [14 points] A survey asked the following question: Do you favor or oppose providing tax-funded vouchers or tax deductions to parents who send their children to private schools? Of the 2010 individuals surveyed, 905 favored the proposal, 60 offered no opinion, and 1045 opposed the proposal, and. Do the data indicate a significant difference in the preferences for the financial support of parents who send their children to private schools? Use a .05 level of significance.

a) State the null and alternative hypotheses? (2 points)

b) What is your conclusion if null hypothesis cannot be rejected? (1 point)

c) What is your conclusion if null hypothesis can be rejected? (1 point)

d) Which probability distribution would you use and what are its parameter values? (2 points)

e) What is the test statistic and its value? Calculate its corresponding p-value? (4 points)

f) State the rejection criteria for the Hypothesis test. (1 point)

g) Conduct p-value based Hypothesis test. What is the decision on the hypothesis test? (1 point)

h) What is your recommendation on “Tax-funded Vouchers or Tax Deductions” based on the survey study results? Why would you recommend in such a manner? (2 points)

3. [18 points] For XYZ Company, the monthly percentages of all shipments received on time over the past 12 periods is: 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83. Two forecasting methods were tried.

Forecasting Method 1

Month

Percentage

Forecast

Forecast Error

Absolute Error

Squared Forecast Error

Absolute Percentage Error

1

80

2

82

3

84

4

83

82.00

5

83

83.00

6

84

83.33

7

85

83.33

8

84

84.00

9

82

84.33

10

83

83.67

11

84

83.00

12

83

83.00

13

Totals

Forecasting Method 2

Month

Percentage

Forecast

Forecast Error

Absolute Error

Squared Forecast Error

Absolute Percentage Error

1

80

2

82

80.00

3

84

81.40

4

83

83.22

5

83

83.07

6

84

83.02

7

85

83.71

8

84

84.61

9

82

84.18

10

83

82.66

11

84

82.90

12

83

83.67

13

Totals

a) Fill the tables above. (5 points)

b) What model of forecasting is being used under Method 1? How are you able to say? (2 points)

c) Why are the forecasted values missing for Months 2 and 3 under Method 1? (2 points)

d) If under Forecasting Method 2, forecast is calculated using the following logic

F3 = 0.7 Y2 + 0.3 F2; F4 = 0.7 Y3 + 0.3 F3; and so on for all subsequent time periods,

Which forecasting method is being used and what is the parameter value? (2 points)

e) What is the forecast for Month 13 under both the methods 1 and 2? (2 points)

f) Calculate all three types of Forecasting Accuracy Measures for both the methods. (3 points)

g) Which forecasting model among the two above would you recommend? And why? (2 points)