Question

I mainly need help with the second part. Thank you in advance!

Starbucks launched its prepaid (debit) Starbucks Card in November 2001. The card, which holds between $5 and $500 can be used at any Starbucks location. Suppose Starbucks management wants to study the reasons why some people purchase debit cards with higher prepaid amounts than do other people. Suppose a study of 25 randomly selected prepaid 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 that customer drinks per day, and the customer’s income.

Amount of Prepaid Card ($)	Age	Cups of Coffee per Day	Days per Month at Starbucks	Income ($1,000)
5	25	1	4	20
25	30	5	12	35
10	27	4	10	30
5	42	5	8	30
15	29	8	11	25
50	25	5	12	60
10	50	3	8	30
15	45	5	6	35
5	32	7	16	25
5	23	1	10	20
20	40	5	18	40
35	35	3	12	40
40	28	3	10	50
15	33	2	12	30
200	40	5	15	65
15	37	1	3	30
40	51	8	10	35
5	20	4	8	25
30	26	5	15	35
100	38	10	19	45
30	27	3	12	35
25	29	6	14	35
25	34	4	10	45
50	30	3	6	55
15	22	5	8	30

a. Using this 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.

b. Rerun your model based on the significant independent variables only and explain the results.

c. What sales implications might be evident from this analysis?

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.

d. How strong is the model?

e. Which independent variables seem to have more promise in predicting how many days per month a customer visits Starbucks?

f. What marketing implications might be evident from this analysis?

Answer 1

(a)

Multiple regression model to predict the amount of pre-paid card by other variables is given as

.. i = 1,2,3,.. 25

Where

APC = Amount of Prepaid Card ($)

CCD = Cups of Coffee per Day

DMS = Days per Month at Starbucks

Income = Income ($1,000)

From the summary output, it is inferred that at 95% confidence ( i.e, at 5% level of significance) the independent variable 'Income($1,000)' is the only significant variable (as p-value = 0.0001 < alpha = 0.05) in the model in predicting the dependent variable 'Amount of Prepaid Card ($)'

(b) Considering the output from (a), we re-run the model only the variable 'Income ($1,000)' and the equation is

  ... i = 1,2,3,.. 25

From the 'Summary Output', it is inferred that

Interpret the Coefficient of the Independent variable 'Income ($1,000)', for a dollar increase in 'Income ($1,000)', the mean change in prepaid amount in the dependent variable 'Amount of Prepaid Card ($)' is going to increase by $2.6584

At 95% confidence (i.e., 5% level of significance) considering F-statistic, independent variable 'Income ($1,000)' is statistically significant in predicting the dependent variable 'Amount of Prepaid Card ($)'

R Square - Coefficient of determination, it is inferred that 57.69% of the total variation in the dependent variable 'Amount of Prepaid Card ($)' is explained by the independent variable 'Income ($1,000)'

(c)

Multiple regression model to predict days per month at Starbucks by Age, Income, and Number of cups of coffee per day is given as below:

... i = 1,2,3,4, .. , 25

Where

DMS = Days per Month at Starbucks

CCD = Cups of Coffee per Day

Income = Income ($1,000)

(d)

From R Square, it is inferred that the independent variables considered were able to explain only 40.70% of the total variation in the dependent variable 'Days per Month at Starbucks'

(e)

From the 'Summary Output' in (c), it is inferred that the independent variable 'Cups of Coffee per Day' is the only statistically significant variable (p-value = 0.0029 < 0.05 level of significance) in explaining the dependent variable 'Days per Month at Starbucks'

(f)

From the 'Summary Output' in (b), considering the coefficient of the independent variable 'Income ($1,000)', for a dollar increase in 'Income ($1,000)', the mean change in prepaid amount in the dependent variable 'Amount of Prepaid Card ($)' is going to increase by $2.6584

From the 'Summary Output' in (c), considering the coefficient of the independent variable 'Cups of Coffee per Day', it is inferred that for an increase in one cup of coffee per day, mean increase in the dependent variable 'Days per Month at Starbucks' is going to be 1 day