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.

Air Canada West Jet

.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 x_{1} and x_{2} but also the square of each x variable and the interaction variable of x_{1} and x_{2}. Interpret the excel output.

Y X_{1} X_{2}

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 x_{1} and the log(x_{1}) to develop a model which predicts log(y). Interpret the results. If x_{1}=500 what does the model predict for the value of y?

Y X_{1}

20415 850

11631 146

17818 521

15303 304

22487 1029

21988 910

16444 242

13245 204

17567 487

12451 192