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STAT 212 Business Statistics II– Term 131

KING FAHD UNIVERSITY OF PETROLEUM & MINERALS

DEPARTMENT OF MATHEMATICS & STATISTICS

DHAHRAN, SAUDI ARABIA

STAT 212: BUSINESS STATISTICS II

Semester 131

Major Exam Three

Wednesday, December 04, 2013

Allowed time 90 minutes

Please circle your instructor’s name and section number:

Instructor / Section Number
Musawar A. Malik / Sec 2: (08:00 –08:50) Sec 5: (11:00 – 11:50)

Raid Anabosi Sec 4: (09:00- 09:50)

Name: Student ID#: Serial #:

Directions:

1)You must show all your work to obtain full credit.

2)Round your answers to at least 4 decimal places.

3)You are allowed to use electronic calculators and other reasonable writing accessories that help write the exam.

4)Do not keep your mobile with you during the exam, turn off your mobile and leave it aside

Question No / Full Marks / Marks Obtained
Q1 / 14
Q2 / 7
Q3 / 15
Total / 36

Q1. (2+2+4+2+4). A study was conducted in a city to determine what variables, if any, are related to family spending. Several variables were explored, including the income, the size of the family, marital status of the homeowner-Whether married =1 and, divorced =0. The data for these four variables for ten households, spending and income are in thousands of dollars. Use the following MINITAB output to answer the following questions.

Regression Analysis: Spending versus Income, Size, Status

The regression equation is

Spending = 5.27 + 0.0841 Income + 0.978 Size + 0.104 Status

Predictor Coef SECoef T P VIF

Constant 5.2713 0.8160 6.46 0.001

Income 0.08413 0.03105 2.71 0.035 3.352

Size 0.9782 0.2284 4.28 0.005 3.497

Status 0.1041 0.4142 0.25 0.810 1.108

S = 0.609595 R-Sq = 96.3% R-Sq(adj) = 94.4%

Analysis of Variance

Source DF SS MS F P

Regression 3 57.770 19.257 51.82 0.000

Residual Error 6 2.230 0.372

Total 9 60.000

Best Subsets Regression: Spending versus Income, Size, Status

Response is Spending

I S

n t

c S a

o i t

m z u

Vars R-Sq R-Sq(adj) Mallows-Cp S e e s

1 91.6 90.6 7.5 0.79216 X

1 83.2 81.1 21.1 1.1219 X

2 96.2 95.2 2.1 0.56734 X X

2 91.7 89.4 9.3 0.84160 X X

3 96.3 94.4 4.0 0.60960 X XX

  1. Predict the spending price of a married family with $30000 income and with size of 6 persons.
  1. Interpret the estimate of slope of marital status.
  1. Construct a 95% confidence interval for the true value of the slope of family size and use it to test the hypothesis that there is no relation between the family spending and the family size.
  1. Do you think that there is collinearity between the independent variables? Explain.
  1. Choose the best model that you think will fit this data set better. Clearly indicate the criterions that you are using to make your choice.

Q2. (5+2). A traffic consultant has analyzed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction

where

y = number of annual fatalities per county

= number of cars registered in the county (in 10,000)

= number of trucks registered in the county (in 1000)

The computer output (based on a random sample of 35 counties) is shown below:

THE REGRESSION EQUATION IS

Predictor

/ Coef / StDev / T
Constant / 69.7 / 41.3 / 1.688
/ 11.3 / 5.1 / 2.216
/ 7.61 / 2.55 / 2.984
/ -1.15 / 0.64 / -1.797
/ -0.51 / 0.20 / -2.55
/ -0.13 / 0.10 / -1.30

S = 15.2R-Sq = 47.2%

  1. Test at the 1% significance level to determine which term is not significant in the model.
  1. What does the coefficient of tell you about the model?

Q3. (3+3+3+3+3). The objective set forth in a recent staff meeting at D. L. Green & Associates is to develop a regression model for predicting company stock price (Y) using several potential independent variables:

X1: Annual 3-S-year growth rate in sales as a percentage; X2: Total sales in millions of dollars for last four quarters;

X3: Profits for last four quarters; X4: Stock price 1 year earlier; X5: Price earnings (P/E) ratio over last four quarters.

The Stock Market for which the company is traded are: Over the Counter (OTC), New York Stock Exchange (NYSE) or NASDAQ.

X6 = 1 if the company stock is traded in NYSE

= 0 otherwise

X7 = 1 if the company stock is traded in NASDAQ

= 0 otherwise

Use the MINITAB output given below to answer the following questions:

The regression equation is

Y = 5.99 + 0.0032 X1 - 0.00243 X2 + 0.0498 X3 + 0.949 X4 + 0.0989 X5

- 1.85 X6 - 7.60 X7

Predictor Coef SE Coef T P VIF

Constant 5.992 3.020 1.98 0.051

X1 0.00315 0.02199 0.14 0.886 1.0

X2 -0.002433 0.001567 -1.55 0.097 1.7

X3 0.04977 0.02075 2.40 0.019 1.9

X4 0.9485 0.1346 7.04 0.000 1.6

X5 0.09889 0.02651 3.73 0.000 1.1

X6 -1.848 2.445 -0.76 0.452 1.1

X7 -7.603 3.619 -2.10 0.039 1.2

S = 9.532 R-Sq = 57.5% R-Sq(adj) = 53.7%

Analysis of Variance

Source DF SS MS F P

Regression 7 9710.4 1387.2 15.27 0.000

Residual Error 79 7177.4 90.9

Total 86 16887.8

Best SubsetsRegression: Y versus X1; X2; X3; X4; X5; X6; X7

Response is Y

X XXXXXX

Vars R-Sq R-Sq(adj) C-p S 1 2 3 4 5 6 7

1 44.9 44.2 19.5 10.465 X

2 46.6 45.4 18.2 10.359 X X

3 53.8 52.1 6.9 9.6984 X X X

4 55.1 52.9 6.5 9.6207 X X X X

5 56.2 53.5 6.5 9.5593 X X X X X

6 57.5 54.3 6.0 9.4731 X X X X X X

7 57.5 53.7 8.0 9.5317 X X X X X X X

  1. How much of the total variation in the stock price can be explained by theses independent variables? Would you conclude that the model is significant at the 2% level? Explain.
  1. Develop a 99% confidence interval for the regression coefficient of the variable X3 and interpret this confidence interval. Based on your finding can you conclude that the (X3) total sales in millions of dollars for last four quarters playing a significant role? Explain.
  1. Which of the independent variables play a significant role in explaining the dependent variable? Explain your answer using 5% level of significance.
  1. Select the best model using the MINITAB output. Clearly justify your selection.
  1. What can you say about the assumptions of regression model, using the MINITAB graph for the residuals?