# Stats 3001 test 2

Solve the following statistical business problems. You must show your work to get full marks. For all problems were an alpha is required use alpha=.01.

Please submit your electronic work through test 2 on the assignment tab in blackboard.

Question 1 (4 marks)

An analyst wishes to know if there is a correlation in share prices for two airlines – Air Canada and West Jet. Determine the correlation coefficient for the data below. Interpret the results of the correlation coefficient.

.75                                          11.92

.76                                          12.09

.84                                          12.25

.85                                          11.85

.86                                          11.78

.86                                          11.74

Question 2 (5 marks)

Calculate the statistical linear regression line for the data below. Interpret the excel output. Use the equation of the line to predict the cost for year 7.

Year                       Cost (\$ millions)

1                                             56

2                                             54

3                                             49

4                                             46

5                                             45

Question 3 (6 marks)

Starbucks has experienced continued rapid growth in recent years. A financial analyst at their corporate head office wanted to determine if they could predict revenue with a predict model using the number of stores, number of drinks offered and average weekly earnings as potential predictors. Using the data below develop a multiple regression model. Interpret the results.

Sales Year            Revenue              Number of Stores            Number of Drinks            Avg Weekly Earnings

1                              400                         676                                         15                                           386

2                              700                         1015                                       15                                           394

3                              1000                       1412                                       18                                           407

4                              1350                       1886                                       22                                           425

5                              1650                       2135                                       27                                           442

6                              2200                       3300                                       27                                           457

7                              2600                       4709                                       30                                           474

Question 4 (8 marks)

A publisher’s information bureau wanted to know if Magazine Advertising Expenditures could be predicted based on household equipment and Supply expenditures. Two models were developed, one using Household Equipment and Supply Expenditures only as a predictor and one using both Household Equipment and Supply Expenditures and (Household Equipment and Supply Expenditures)2. Develop , interpret and compare these models to each other. Which model is better? Do the model results suggest a different model may be required? Why or why not?

Total Magazine Advertising Exp (\$millions)        Household Equipment and Supply Exp (\$millions)

1193                                                                                       34

2846                                                                                       65

4668                                                                                       98

5120                                                                                       93

5943                                                                                       102

6644                                                                                       103

Question 5 (7 marks)

A market analyst for a fast food restaurant wanted to determine if the amount spent at restaurant could be predicted based on a customer’s age and gender. Develop the appropriate model using the data below and interpret the results. If a 20 year old male walks into the store what would the model predict the customer will spend?

Spend Amount (\$)           Age (years)                         Gender (1=Male,0=Female)

16.80                                     27                                           1

13.20                                     16                                           0

14.70                                     13                                           0

15.40                                     11                                           1

11.10                                     17                                           0

16.20                                     19                                           1

14.90                                     24                                           1

13.30                                     21                                           0

17.80                                     16                                           1

17.10                                     23                                           1

14.30                                     18                                           0

13.90                                     16                                           0

Question 6 (6 marks)

Use the data below to develop a model which predicts y. In your model include not only x1 and x2 but also the square of each x variable and the interaction variable of x1 and x2. Interpret the excel output.

Y                              X1            X2

2002                       10           3

1747                       5              14

1980                       8              4

1902                       7              4

1842                       6              7

1883                       7              6

1697                       4              21

2021                       11           4

Question 7 (8 marks)

Use both x1 and the log(x1) to develop a model which predicts log(y). Interpret the results. If x1=500 what does the model predict for the value of y?

Y                              X1

20415                    850

11631                    146

17818                    521

15303                    304

22487                    1029

21988                    910

16444                    242

13245                    204

17567                    487

12451                    192

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