Using Regression to Analyze Business

Business Statistics

Regression

Variables Entered/Removeda

Model

Variables Entered

Variables Removed

Income ($1,000), Cups of Coffee per Day, Age, Days per Month at Starbucksb

Dependent Variable: Amount of Prepaid Card $

All requested variables entered.

Model Summaryb

Model

R

R Square

Error of the Estimate

Durbin-Watson

Predictors: (Constant), Income ($1,000), Cups of Coffee per Day, Age, Days per Month at Starbucks

Dependent Variable: Amount of Prepaid Card $

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

Regression

Residual

Total

Dependent Variable: Amount of Prepaid Card $

Predictors: (Constant), Income ($1,000), Cups of Coffee per Day, Age, Days per Month at Starbucks

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

10.949

10.562

1.037

.312

Age

.415

.270

.313

1.535

.140

.873

1.146

Days per Month at Starbucks

1.005

.692

.362

1.452

.162

.584

1.712

Cups of Coffee per Day

-2.590

1.235

-.520

-2.096

.049

.590

1.696

Income ($1,000)

.166

.169

.201

.984

.337

.873

1.146

a. Dependent Variable: Amount of Prepaid Card $

Collinearity Diagnosticsa

Model

Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

Age

Days per Month at Starbucks

Cups of Coffee per Day

Income ($1,000)

1

1

4.683

1.000

.00

.00

.00

.00

.00

2

.152

5.546

.02

.03

.03

.43

.13

3

.084

7.451

.03

.23

.16

.03

.39

4

.056

9.109

.08

.00

.51

.40

.47

5

.024

14.014

.87

.74

.28

.14

.00

a. Dependent Variable: Amount of Prepaid Card $

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

17.48

42.97

29.96

5.823

25

Residual

-21.080

19.592

.000

9.494

25

Std. Predicted Value

-2.144

2.235

.000

1.000

25

Std. Residual

-2.027

1.884

.000

.913

25

a. Dependent Variable: Amount of Prepaid Card $

Regression

Variables Entered/Removeda

Model

Variables Entered

Variables Removed

Method

1

Gender, Age, Income ($1,000), Cups of Coffee per Day, Days per Month at Starbucksb

Enter

a. Dependent Variable: Amount of Prepaid Card $

b. All requested variables entered.

Model Summaryb

Model

R

R Square

Adjusted R. Square

Std. Error of the Estimate

Durbin-Watson

1

.532a

.283

.095

10.598

1.655

a. Predictors: (Constant), Gender, Age, Income ($1,000), Cups of Coffee per Day, Days per Month at Starbucks

b. Dependent Variable: Amount of Prepaid Card $

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

5

1.501

.236b

Residual

19

Total

24

a. Dependent Variable: Amount of Prepaid Card $

b. Predictors: (Constant), Gender, Age, Income ($1,000), Cups of Coffee per Day, Days per Month at Starbucks

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

12.669

11.280

1.123

.275

Age

.421

.276

.318

1.528

.143

.871

1.148

Days per Month at Starbucks

.888

.741

.320

1.198

.246

.529

1.891

Cups of Coffee per Day

-2.636

1.262

-.530

-2.089

.050

.587

1.704

Income ($1,000)

.185

.176

.223

1.050

.307

.836

1.197

Gender

-2.393

4.692

-.110

-.510

.616

.818

1.223

a. Dependent Variable: Amount of Prepaid Card $

Collinearity Diagnosticsa

Model

Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

Age

Days per Month at Starbucks

Cups of Coffee per Day

Income ($1,000)

Gender

1

1

5.158

1.000

.00

.00

.00

.00

.00

.01

2

.566

3.020

.00

.00

.01

.02

.00

.61

3

.118

6.602

.01

.01

.00

.54

.25

.21

4

.080

8.045

.05

.31

.12

.01

.29

.08

5

.055

9.664

.06

.02

.52

.31

.46

.03

6

.023

15.093

.88

.65

.35

.12

.00

.06

a. Dependent Variable: Amount of Prepaid Card $

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

18.19

44.45

29.96

5.927

25

Residual

-20.423

20.625

.000

9.429

25

Std. Predicted Value

-1.986

2.444

.000

1.000

25

Std. Residual

-1.927

1.946

.000

.890

25

a. Dependent Variable: Amount of Prepaid Card $

1. Starbucks Debit Card

Multiple regression was used to explore how well the amount of the prepaid card can be predicted by other variables, and which variables show the most promise for generating a prediction. The results of the regression indicated that the four predictors explained only .27 of the variance (R2 = .27, F = 1.881, p >.05). The coefficients for the independent variables are as follows: Age, ? = .313; Days per month, ? =.362; Cups of Coffee per day, ? = -.520; Income ($1,000) ? = .201. Of these, the number of cups of coffee per day is significantly predicted the amount of money on the prepaid Starbucks cards purchased by the customers (? = -.520, p

2. Prediction of Days per Month at Starbucks

The results of the regression indicated that the four predictors (debit card amounts were not included) explained only .47 of the variance (R2 = .471, F = 4.457, p ?.01). This model is a better fit, but ideally we would look for R2 to be in the mid to high 90s. The coefficients for the independent variables are as follows: Age, ? = -.138; Gender, ? =-.248; Cups of Coffee per day, ? = -.516; Income ($1,000) ? = .268. Days per month Number of cups of coffee consumed per day predicted the days per month at Starbucks (? = .516, p

Regression

Model Summaryb

Model

R

R Square

Adjusted R. Square

Std. Error of the Estimate

Durbin-Watson

1

.687a

.471

.366

3.197

1.384

a. Predictors: (Constant), Gender, Age, Income ($1,000), Cups of Coffee per Day

b. Dependent Variable: Days per Month at Starbucks

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

4

45.545

4.457

.010b

Residual

20

10.219

Total

24

a. Dependent Variable: Days per Month at Starbucks

b. Predictors: (Constant), Gender, Age, Income ($1,000), Cups of Coffee per Day

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

5.73

17.15

10.76

2.755

25

Residual

-5.260

7.960

.000

2.918

25

Std. Predicted Value

-1.826

2.319

.000

1.000

25

Std. Residual

-1.645

2.490

.000

.913

25

a. Dependent Variable: Days per Month at Starbucks

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

6.804

3.043

2.236

.037

Age

-.066

.082

-.138

-.806

.430

.899

1.112

Cups of Coffee per Day

.926

.320

.516

2.897

.009

.833

1.201

Income ($1,000)

.080

.050

.268

1.599

.125

.942

1.061

Gender

-1.949

1.346

-.248

-1.448

.163

.903

1.107

a. Dependent Variable: Days per Month at Starbucks

Collinearity Diagnosticsa

Model

Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

Age

Cups of Coffee per Day

Income ($1,000)

Gender

1

1

4.264

1.000

.00

.00

.01

.01

.01

2

.515

2.876

.00

.00

.05

.00

.73

3

.118

6.006

.02

.01

.79

.28

.21

4

.074

7.592

.08

.25

.15

.65

.03

5

.029

12.175

.90

.74

.00

.07

.00

a. Dependent Variable: Days per Month at Starbucks

Charts

3. Predict Sales Revenue By Number Of Drinks Sold

Multiple regression was used to explore the impact a number of variables have on revenue generation. The results of the regression indicated that the four predictors explained 1.000 of the variance (R2 = 1.000, F = 3084.3, p >.001). The coefficients for the independent variables are as follows: Average Weekly Earnings, ? = 1.392; Sales Year, ? =.118; Number of Stores, ? = -.006; Number of Drinks ? = -.516. The Durbin-Watson statistic is 3.243, which indicates there is a multicollinearity problem. The relation between the tolerance and the VIF is VIF=1/Tolerance. The variance inflation factor (VIF) for all variables is quite high which indicates a problem with multicollinearity. However, the tolerance levels, which reflect how much of the variance can be accounted for with each individual variable are all less than 0.3, so they can be discounted as inconsequential to the model outcomes. The model needs to be corrected for autocorrelation. In addition, other models should be generated to test the impact of eliminating some of the variables. For example, the beta of Average Weekly Earnings is higher than the betas for the other variables, and two of the variables (# of Stores; # of Drinks) have negative signs, which signals a strong predictive relationship with revenue generation. Growth in the number of stores remains one of the most interesting of the variables as Starbucks has at times been plagued by its own cannibalization of stores and rapid expansion as a competitive strategy. The diversification into increasingly more types of drinks is also a good variable to watch, however, product diversification is a key strategy for moving into different markets. Year-over-year same store revenue is missing from this analysis, yet it is relevant to consideration of stores expansion.

Regression

Model Summaryb

Model

R

R Square

Adjusted R. Square

Std. Error of the Estimate

Durbin-Watson

1

1.000a

1.000

1.000

17.534

3.243

a. Predictors: (Constant), Average Weekly Earnings, # of Stores, # of Drinks, Sales Year

b. Dependent Variable: Revenue

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

3792956.548

4

948239.137

.000b

Residual

2

Total

3793571.429

6

a. Dependent Variable: Revenue

b. Predictors: (Constant), Average Weekly Earnings, # of Stores, # of Drinks, Sales Ye

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

-11620.134

-4.779

.041

Sales Year

43.409

51.238

.118

.847

.486

.004

# of Stores

-.003

.040

-.006

-.079

.944

.016

62.311

# of Drinks

-66.603

14.663

-.516

-4.542

.045

.006

Average Weekly Earnings

33.612

7.017

1.392

4.790

.041

.001

a. Dependent Variable: Revenue

Coefficient Correlationsa

Model

Average Weekly Earnings

# of Stores

# of Drinks

Sales Year

1

Correlations

Average Weekly Earnings

1.000

-.902

-.923

-.905

# of Stores

-.902

1.000

.885

.685

# of Drinks

-.923

.885

1.000

.692

Sales Year

-.905

.685

.692

1.000

Covariances

Average Weekly Earnings

49.237

-.254

-94.989

-325.236

# of Stores

-.254

.002

.519

1.406

# of Drinks

-94.989

.519

Sales Year

-325.236

1.406

a. Dependent Variable: Revenue

Collinearity Diagnosticsa

Model

Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

Sales Year

# of Stores

# of Drinks

Average Weekly Earnings

1

1

4.769

1.000

.00

.00

.00

.00

.00

2

.216

4.698

.00

.00

.01

.00

.00

3

.014

18.618

.00

.02

.14

.01

.00

4

.002

54.307

.00

.16

.04

.15

.00

5

2.917E-6

1.00

.82

.81

.85

1.00

a. Dependent Variable: Revenue

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

7

Residual

-17.147

13.350

.000

10.123

7

Std. Predicted Value

-1.281

1.494

.000

1.000

7

Std. Residual

-.978

.761

.000

.577

7

a. Dependent Variable: Revenue

Charts

4. Contribution of Gender to Model