Assignment

Question 1

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

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

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

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

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

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

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