# **SPSS Help: Learn How to Work on a Linear Regression Case Study Using SPSS**

- Starbucks is a resounding restaurant success story. Beginning with its first coffee house in 1971, Starbucks has grown to more than 5,200 locations with projections of reaching 10,000 by the year 2005. Opening up its first international outlet in the mid 1990s, Starbucks now operates in more than 22 countries (900 coffee houses) outside of North America. Besides selling beverages, pastries, confections, and coffee-related accessories and equipment at its retail outlets, Starbucks also purchases and roasts high-quality coffee beans in several locations. The company’s objective is to become the most recognized and respected brand in the world. Starbucks maintains a strong environmental orientation and is committed to taking a leadership position environmentally. In addition, the company has won awards for corporate social responsibility through its community building programs, its strong commitment to its origins (coffee producers, family, community), and the Starbucks Foundation, which is dedicated to creating hope, discovery, and opportunity in the communities where Starbucks resides.

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In November 2001, Starbucks launched its prepaid (debit) Starbucks card. The card, which holds between $5 and $500, can be used virtually at any Starbucks location. The card was so popular when it first was released that many stores ran out. By mid-2002, Starbucks had activated more than 5 million of these cards. It is believed that the card accounted for a large portion of the company’s 7% same store increase in sales in early 2002 and that it is responsible for attracting many new patrons to the store. As customers “reload” the cards, it appears they are placing more money on them than the initial value of the card.

### Discussion of the Problem

a) Starbucks enjoyed considerable success with its debit cards, which they sell for $5 to $500. Since the card was introduced in November 2001, sales revenue increased. Suppose Starbucks management wants to study the reasons why some people purchase debit cards with higher prepaid amounts than to other people. Suppose a study of 25 randomly selected prepaid card purchasers is taken. Respondents are asked the amount of the prepaid card, the customer’s age, the number of days per month the customer makes a purchase at Starbucks, the number of cups of coffee the customer drinks per day, and the customer’s income. The data follow. Using these data, develop a multiple regression model to study how well the amount of the prepaid card can be predicted by the other variables and which variables seem to be more promising in doing the prediction. What sales implications might be evident from this analysis?

Amount of Prepaid Card ($) |
Age |
Days per Month at Starbucks |
Cups of Coffee per Day |
Increase ($1,000) |

5 |
25 |
4 |
1 |
20 |

25 |
30 |
12 |
5 |
35 |

10 |
27 |
10 |
4 |
30 |

5 |
42 |
8 |
5 |
30 |

15 |
29 |
11 |
8 |
25 |

50 |
25 |
12 |
5 |
60 |

10 |
50 |
8 |
3 |
30 |

15 |
45 |
6 |
5 |
35 |

5 |
32 |
16 |
7 |
25 |

5 |
23 |
10 |
1 |
20 |

20 |
40 |
18 |
5 |
40 |

35 |
35 |
12 |
3 |
40 |

40 |
28 |
10 |
3 |
50 |

15 |
33 |
12 |
2 |
30 |

200 |
40 |
15 |
5 |
80 |

15 |
37 |
3 |
1 |
30 |

40 |
51 |
10 |
8 |
35 |

5 |
20 |
8 |
4 |
25 |

30 |
26 |
15 |
5 |
35 |

100 |
38 |
19 |
10 |
45 |

30 |
27 |
12 |
3 |
35 |

25 |
29 |
14 |
6 |
35 |

25 |
34 |
10 |
4 |
45 |

50 |
30 |
6 |
3 |
55 |

15 |
22 |
8 |
5 |
30 |

**Solution: **We are going to use SPSS to run a multiple regression:

First, we have some descriptive statistics:

This indicates that the multiple correlation coefficient is \(R = 0.869\), which is significantly different from zero (according to the Person’s critical value). *That implies that there exists a significant linear association between the dependent variable and the predictors.*

Also, the coefficient of determination is \({{R}^{2}}=0.755\) which implies that 75.5% of variation of the dependent variable is explained by the regression.

## SPSS ANOVA table:

This table indicates (\(p < .001\)) a significant p-value, which means that the variables do a good job explaining the dependent variable. In other words, the overall model makes sense because *we reject the null hypothesis that all the coefficients of the regression are zero*.

Now we present the table with the coefficients of the regression, p-values and confidence intervals:

The p-values indicate that the only coefficients of the regression which are significantly different from zero are the Income ($1000) (\(p < .001\)) and the constant (\(p = .001\)). *That means that among all the studied variables, the one that determines the dependent significantly is the Income.*

Finally, we present the collinearity analysis:

All of the condition indices are less than 15, which is not enough evidence of collinearity.

b) Suppose marketing wants to be able to profile frequent visitors to a Starbucks store. Using the same data set already provided, develop a multiple regression model to predict days per month at Starbucks by Age, Income, and Number of cups of coffee per day. How strong is the model? Which particular independent variables seem to have more promise in predicting how many days per month a customer visits Starbucks? What marketing implications might be evident from this analysis?

**Solution: ** Again, we use SPSS to perform a multiple regression analysis.

This indicates that the multiple correlation coefficient is \(R = 0.645\), which is not too high, but significantly different from zero (according to the Person’s critical value). *That implies that there exists a significant linear association between the dependent variable and the predictors, even though it could be rather weak. *Also, the coefficient of determination is \({{R}^{2}}=0.41\) which implies that 41.6% of variation of the dependent variable is explained by the regression.

Now we exhibit the ANOVA table:

This table indicates (\(p = .009\)) a significant p-value, which means that the variables do good job explaining the dependent variable. In other words, the overall model makes sense because *we reject the null hypothesis that all the coefficients of the regression are zero*.

Now we present the table with the coefficients of the regression, p-values and confidence intervals:

The p-values indicate that the only coefficient of the regression which is significantly different from zero is the Cups of Coffee per day (\(p = .003\)). *That means that among all the studied variables, the one that determines the dependent significantly is the Cups of Coffee per day. This suggests that if we increase the daily number of cups of coffee per client, we’ll increase the number of days per month at Starbucks.*

c) Over the past decade or so, Starbucks has grown quite rapidly. As they add stores and increase the number of drinks, their sales revenues increase. In reflecting about this growth, think about some other variables that might be related to the increase in Starbucks sales revenues. Some data for the past seven years on the number of Starbucks stores (worldwide), approximate sales revenue (in $ millions), number of different drinks sold, and average weekly earnings of U.S. production workers are given here. Most figures are approximate. Develop a multiple regression model to predict sales revenue by number of drinks sold, number of stores, and average weekly earnings. How strong is the model? What are the key predictors, if any? How might this analysis help Starbucks management in attempting to determine what drives sales revenues?

Sales Year |
Revenue |
Number of Stores |
Number of Drinks |
Average 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 |

## SPSS Multiple Regression Analysis

This indicates that the multiple correlation coefficient is \(R=1\), which is exceptionally high, and significantly different from zero. *That implies that there exists a significant linear association between the dependent variable and the predictor. *Also, the coefficient of determination is \({{R}^{2}}=1\) which implies that 100% of variation of the dependent variable is explained by the regression.

Now we exhibit the ANOVA table:

This table indicates (\(p < .001\)) a significant p-value, which means that the variables do good job overall explaining the dependent variable. In other words, the overall model makes sense because *we have enough evidence to reject the null hypothesis that all the coefficients of the regression are zero*.

Now we present the table with the coefficients of the regression, p-values and confidence intervals:

The p-values indicate that the coefficients of the regression which is significantly different from zero are the Number of Drinks (\(p = .005\)), the Average weekly earnings (\(p = .001\)) and the constant (\(p = .001\)). *That means that among all the studied variables, the ones that determine the dependent significantly are the Number of Drinks per day and the Average Weekly earnings. *Interesting enough is the fact that the number of drinks sold affects negatively the revenue.

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