Chapter 4Chapter 4

Multiple Regression Multiple Regression

Multiple Regression OverviewMultiple Regression Overview

• What is it?What is it?

• Why use it?Why use it?

Multiple RegressionMultiple Regression

Y’ = bY’ = b0 0 + b + b11XX11 + b + b22XX22 + . . . + b + . . . + bnnXXn n + e + e

YY = Dependent Variable = # of credit cards = Dependent Variable = # of credit cards

bb00 = intercept (constant) = constant number of = intercept (constant) = constant number of credit credit cards independent of family size and income.cards independent of family size and income.

bb11 = change in credit card usage associated with = change in credit card usage associated with unitunit

change in family size (regression coefficient).change in family size (regression coefficient).

bb22 = change in credit card usage associated with = change in credit card usage associated with unitunit

change in income (regression coefficient).change in income (regression coefficient).

XX11 = family size = family size

XX22 = income = income

e e = prediction error (residual)= prediction error (residual)

Variate (Y’) = XVariate (Y’) = X11bb11 + X + X22bb22 + . . . + X + . . . + Xnnbbnn

A variate value (Y’) is calculated for each respondent.A variate value (Y’) is calculated for each respondent.

The Y’ vaThe Y’ valuelue is a is a linear combinationlinear combination of the entire set of of the entire set of variables that best achieves the statistical objective. variables that best achieves the statistical objective. With regression, the variate value is the predicted With regression, the variate value is the predicted dependent variable.dependent variable.

YX1

X2

X3

Example of a “Business-to-Business” Example of a “Business-to-Business” Application of Multiple RegressionApplication of Multiple Regression

1.1. Product QualityProduct Quality

2.2. Delivery CommitmentsDelivery Commitments

3.3. Problem ResolutionProblem Resolution

4.4. Competitive PricesCompetitive Prices

5.5. Quality AssuranceQuality Assurance

6.6. Technical AssistanceTechnical Assistance

7.7. Creative Pricing / TermsCreative Pricing / Terms

8.8. Technical AlliancesTechnical Alliances

9.9. InvoicingInvoicing

10.10. Product LineProduct Line

Outcome Measures:Outcome Measures:

1)1) Future PurchaseFuture Purchase

2)2) RecommendRecommend

3)3) SatisfactionSatisfaction

Performance MeasuresPerformance Measures

What Can We Do WithWhat Can We Do WithMultiple Regression?Multiple Regression?

1.1. Determine the statistical significance of the Determine the statistical significance of the attempted prediction.attempted prediction.

2.2. Determine the strength of association Determine the strength of association between the single dependent variable and between the single dependent variable and the multiple independent variables.the multiple independent variables.

3.3. Identify the relative importance of each of Identify the relative importance of each of the multiple independent variables in the multiple independent variables in predicting the single metric dependent predicting the single metric dependent variable.variable.

4.4. Predict the values of the dependent variable Predict the values of the dependent variable from the values of the multiple independent from the values of the multiple independent variables.variables.

Using Multiple RegressionUsing Multiple Regression

• Sources of variables?Sources of variables?

• Number of independent variables?Number of independent variables? Is More Better ?Is More Better ?

• Method of variable entry?Method of variable entry?

• Interpretation of regressionInterpretation of regression

functions?functions?

Regression Variables?Regression Variables?

Sources Sources ::

Prior Research ?Prior Research ?

Practice – Current Business Practice – Current Business

Situation ?Situation ?

Theoretical Model ?Theoretical Model ?

Intuition ?Intuition ?

Regression Variables ?Regression Variables ?

IssuesIssues : : Measurement Error –Measurement Error – Both Dependent Both Dependent

& & Independents.Independents.

Specification Error –Specification Error – Independents only. Independents only.

•Too Few:Too Few:lowers prediction.lowers prediction.introduces bias.introduces bias.

•Too Many:Too Many: Reduces parsimony.Reduces parsimony. Masks effects of other variables.Masks effects of other variables.

Variable Selection Approaches:Variable Selection Approaches:

• Confirmatory (Simultaneous).Confirmatory (Simultaneous).

• Sequential Search Methods:Sequential Search Methods: Stepwise (variables not removed once Stepwise (variables not removed once

includedincluded

in regression equation).in regression equation). Forward Inclusion & Backward Forward Inclusion & Backward

Elimination.Elimination.

• Combinatorial (All-Possible-Subsets).Combinatorial (All-Possible-Subsets).

Interpretation ofInterpretation ofRegression Results:Regression Results:

• Coefficient of Determination. Coefficient of Determination.

• Regression Coefficients Regression Coefficients (Unstandardized – (Unstandardized –

bivariate).bivariate).

• Beta Coefficients Beta Coefficients

(Standardized).(Standardized).

• Variables Entered.Variables Entered.

• Multicollinearity ??Multicollinearity ??

Statistical vs. Practical Significance ?Statistical vs. Practical Significance ?

The F statistic is used to determine if the overall regression The F statistic is used to determine if the overall regression model is statistically significant. If the F statistic is significant, it means model is statistically significant. If the F statistic is significant, it means it is unlikely your sample will produce a large Rit is unlikely your sample will produce a large R22 when the population R when the population R22 is actually zero. To be considered statistically significant, a rule of is actually zero. To be considered statistically significant, a rule of thumb is there must be <.05 probability the results are due to chance. thumb is there must be <.05 probability the results are due to chance.

If the RIf the R22 is statistically significant, we then evaluate the strength is statistically significant, we then evaluate the strength of the linear association between the dependent variable and the several of the linear association between the dependent variable and the several independent variables. Rindependent variables. R22, also called the coefficient of determination, is , also called the coefficient of determination, is used to measure the strength of the overall relationship. It represents used to measure the strength of the overall relationship. It represents the amount of variation in the dependent variable associated with all of the amount of variation in the dependent variable associated with all of the independent variables considered together (it also is referred to as a the independent variables considered together (it also is referred to as a measure of the goodness of fit). Rmeasure of the goodness of fit). R22 ranges from 0 to 1.0 and represents ranges from 0 to 1.0 and represents the amount of the dependent variable “explained” by the independent the amount of the dependent variable “explained” by the independent variables combined. A large Rvariables combined. A large R22 indicates the straight line works well indicates the straight line works well while a small Rwhile a small R22 indicates it does not work well. indicates it does not work well.

Even though an REven though an R22 is statistically significant, it does not mean it is statistically significant, it does not mean it is practically significant. We also must ask whether the results are is practically significant. We also must ask whether the results are meaningful. For example, is the value of knowing you have explained 4 meaningful. For example, is the value of knowing you have explained 4 percent of the variation worth the cost of collecting and analyzing the percent of the variation worth the cost of collecting and analyzing the data? data?

Variable Description Variable Type

Work Environment MeasuresX1 I am paid fairly for the work I do. MetricX2 I am doing the kind of work I want. MetricX3 My supervisor gives credit an praise for work well done. MetricX4 There is a lot of cooperation among the members of my work group. MetricX5 My job allows me to learn new skills. MetricX6 My supervisor recognizes my potential. MetricX7 My work gives me a sense of accomplishment. MetricX8 My immediate work group functions as a team. MetricX9 My pay reflects the effort I put into doing my work. MetricX10 My supervisor is friendly and helpful. MetricX11 The members of my work group have the skills and/or training

to do their job well. MetricX12 The benefits I receive are reasonable. MetricRelationship MeasuresX13 Loyalty – I have a sense of loyalty to Samouel’s restaurant. MetricX14 Effort – I am willing to put in a great deal of effort beyond that

expected to help Samouel’s restaurant to be successful. MetricX15 Proud – I am proud to tell others that I work for Samouel’s restaurant. MetricClassification VariablesX16 Intention to Search MetricX17 Length of Time an Employee NonmetricX18 Work Type = Part-Time vs. Full-Time NonmetricX19 Gender NonmetricX20 Age NonmetricX21 Performance Metric

Description of Employee Survey VariablesDescription of Employee Survey Variables

Variable Description Variable Type

Restaurant PerceptionsX1 Excellent Food Quality MetricX2 Attractive Interior MetricX3 Generous Portions MetricX4 Excellent Food Taste MetricX5 Good Value for the Money MetricX6 Friendly Employees MetricX7 Appears Clean & Neat MetricX8 Fun Place to Go MetricX9 Wide Variety of menu Items MetricX10 Reasonable Prices MetricX11 Courteous Employees MetricX12 Competent Employees MetricSelection Factor RankingsX13 Food Quality NonmetricX14 Atmosphere NonmetricX15 Prices NonmetricX16 Employees NonmetricRelationship VariablesX17 Satisfaction MetricX18 Likely to Return in Future MetricX19 Recommend to Friend MetricX20 Frequency of Patronage NonmetricX21 Length of Time a Customer NonmetricClassification VariablesX22 Gender NonmetricX23 Age NonmetricX24 Income NonmetricX25 Competitor NonmetricX26 Which AD Viewed (#1, 2 or 3) NonmetricX27 AD Rating MetricX28 Respondents that Viewed Ads Nonmetric

Description of Customer Survey VariablesDescription of Customer Survey VariablesVS.VS.

Selected Variables from Samouel’s Customer SurveySelected Variables from Samouel’s Customer Survey

XX11 – Excellent Food Quality – Excellent Food Quality Strongly Strongly Strongly Strongly

Disagree Disagree Agree Agree

1 2 3 4 5 6 7 1 2 3 4 5 6 7

XX44 – Excellent Food Taste – Excellent Food Taste Strongly Strongly Strongly Strongly

Disagree Disagree Agree Agree

1 2 3 4 5 6 7 1 2 3 4 5 6 7

XX99 – Wide Variety of Menu Items – Wide Variety of Menu Items Strongly Strongly

Strongly Strongly Disagree Disagree Agree Agree

1 2 3 4 5 6 1 2 3 4 5 6 77

XX1818 – How likely are you to return to – How likely are you to return to

Samouel’s restaurant in the future?Samouel’s restaurant in the future?Definitely Will Definitely Definitely Will Definitely

Will Will Not Return Return Not Return Return 1 2 3 4 1 2 3 4 5 6 7 5 6 7

Using SPSS to Compute a Multiple Regression Using SPSS to Compute a Multiple Regression Model:Model:

We want to compare Samouel’s customers’ perceptions with We want to compare Samouel’s customers’ perceptions with those of Gino’s, so go to the Data pull-down menu to split the sample. those of Gino’s, so go to the Data pull-down menu to split the sample. Scroll down and click on Split File, then on Compare Groups. Highlight Scroll down and click on Split File, then on Compare Groups. Highlight variable Xvariable X2525 and move it into the box labeled “Groups based on:” and then and move it into the box labeled “Groups based on:” and then

click OK. Now you can run the regression and compare Samouel’s and click OK. Now you can run the regression and compare Samouel’s and Gino’s. Gino’s.

The SPSS click through sequence is ANALYZE The SPSS click through sequence is ANALYZE REGRESSION REGRESSION LINEAR. Highlight X LINEAR. Highlight X1818 and move it to the dependent variables box. and move it to the dependent variables box.

Highlight XHighlight X11, X, X4 4 and Xand X99 and move them to the independent variables box. and move them to the independent variables box.

Use the default “Enter” in the Methods box. Click on the Statistics button Use the default “Enter” in the Methods box. Click on the Statistics button and use the defaults for “Estimates” and “Model Fit”. Next click on and use the defaults for “Estimates” and “Model Fit”. Next click on “Descriptives” and then Continue. There are several other options you “Descriptives” and then Continue. There are several other options you could select at the bottom of this dialog box but for now we will use the could select at the bottom of this dialog box but for now we will use the program defaults. Click on “OK” at the top right of the dialog box to run program defaults. Click on “OK” at the top right of the dialog box to run the regression. the regression.

To run stepwise multiple regressionTo run stepwise multiple regression, follow the same procedure , follow the same procedure as described above except go to the “Methods” box and where it has as described above except go to the “Methods” box and where it has “Enter” as the default click on the arrow box and go to “Stepwise” and “Enter” as the default click on the arrow box and go to “Stepwise” and click on it. Then click on “OK” at the top right of the dialog box to run the click on it. Then click on “OK” at the top right of the dialog box to run the stepwise regression. stepwise regression.

Multiple Regression Dialog BoxesMultiple Regression Dialog Boxes

Multiple Regression OutputMultiple Regression Output

Adjusted R-Square = reduces the R2 by taking into account the sample size and the number of independent variables in the regression model (It becomes smaller as we have fewer observations per independent variable).

Standard Error of the Estimate (SEE) = a measure of the accuracy of the regression predictions. It estimates the variation of the dependent variable values around the regression line. It should get smaller as we add more independent variables, if they predict well.

R-Square = the amount of variation in Y explained by the X’s.

Multiple Regression Output continued . . .Multiple Regression Output continued . . .

Sum of Squared Errors (SSE) = the variance in the dependent variable not accounted for by the regression model = residual. The objective is to obtain the smallest possible sum of squared errors as a measure of prediction accuracy.

Degrees of freedom (df)  = the total number of observations minus the number of estimated parameters. For example, in estimating a regression model with a single independent variable, we estimate two parameters, the intercept (b0) and a regression coefficient for the independent variable (b1). If the number of degrees of freedom is small, the resulting prediction is less generalizable. Conversely, a large degrees-of-freedom value indicates the prediction is fairly “robust” with regard to being representative of the overall sample of respondents. Total Sum of Squares (SST) = total

amount of variation that exists to be explained by the independent variables. TSS = the sum of SSE and SSR.

Sum of Squares Regression (SSR) = the amount of improvement in explanation of the dependent variable attributable to the independent variables.

Multiple Regression Output Multiple Regression Output continued . . . continued . . .

Beta interpretation = for every unit the Samouel’s X1 beta increases, X18 (dependent variable) will increase by .324 units.

Constant term (b0) = also referred to as the intercept, it is the value on the Y axis (dependent variable axis) where the line defined by the regression equation crosses the axis.

Only significant betas are interpreted (=/> .05).

Multiple RegressionMultiple RegressionLearning CheckpointLearning Checkpoint

1.1. When should multiple regression be When should multiple regression be used?used?

2.2. Why should multiple regression be Why should multiple regression be used?used?

3.3. What level of statistical significance What level of statistical significance and and

RR2 2 would justify use of multiplewould justify use of multiple

regression?regression?

4.4. How do you use regression How do you use regression coefficients?coefficients?

Advanced Topics Advanced Topics in Multiple Regressionin Multiple Regression

MulticollinearityMulticollinearity

Dummy Dummy

VariablesVariables

AssumptionsAssumptions

. . . . is the . . . . is the

correlation among correlation among

the independent the independent

variables.variables.

MulticollinearityMulticollinearity

Multicollinearity DiagnosticsMulticollinearity Diagnostics::

• Variance Inflation Factor (VIF)Variance Inflation Factor (VIF) – measures how much the – measures how much the variance of the regression coefficients is inflated by variance of the regression coefficients is inflated by multicollinearity problems. If VIF equals 0, there is no multicollinearity problems. If VIF equals 0, there is no correlation between the independent measures. correlation between the independent measures. A VIF measure A VIF measure of 1 is an indication of some association between predictor of 1 is an indication of some association between predictor variables, but generally not enough to cause problems. A maximum variables, but generally not enough to cause problems. A maximum acceptable VIF value would be 5.0; anything higher would indicate a acceptable VIF value would be 5.0; anything higher would indicate a problem with multicollinearity.problem with multicollinearity.

• Tolerance Tolerance – the amount of variance in an independent – the amount of variance in an independent variable that is not explained by the other independent variable that is not explained by the other independent variables. If the other variables explain a lot of the variance of variables. If the other variables explain a lot of the variance of a particular independent variable we have a problem with a particular independent variable we have a problem with multicollinearity. Thus, small values for tolerance indicate multicollinearity. Thus, small values for tolerance indicate problems of multicollinearity. The minimum cutoff value for problems of multicollinearity. The minimum cutoff value for tolerance is typically .20. That is, the tolerance value must be tolerance is typically .20. That is, the tolerance value must be smaller than .20 to indicate a problem of multicollinearity.smaller than .20 to indicate a problem of multicollinearity.

Using SPSS to Examine MulticollinearityUsing SPSS to Examine Multicollinearity::

The SPSS click through sequence is: ANALYZE The SPSS click through sequence is: ANALYZE REGRESSION REGRESSION LINEAR. Go to Samouel’s employee LINEAR. Go to Samouel’s employee survey data and click on Xsurvey data and click on X13 13 – Loyalty and move it to the – Loyalty and move it to the

Dependent Variables box. Click on variables XDependent Variables box. Click on variables X11 to X to X1212 and and

move them to the Independent Variables box. The box move them to the Independent Variables box. The box labeled “Method” has ENTER as the default and we will labeled “Method” has ENTER as the default and we will use it. Click on the “Statistics” button and use the use it. Click on the “Statistics” button and use the “Estimates” and “Model fit” defaults. Click on “Estimates” and “Model fit” defaults. Click on “Descriptives” and “Collinearity diagnostics” and then “Descriptives” and “Collinearity diagnostics” and then “Continue” and “OK” to run the regression. “Continue” and “OK” to run the regression.

. . . . a nonmetric independent

variable that has two (or more)

distinct levels, that are coded

0 and 1.

Dummy VariableDummy Variable

Selected Variables from Employee Selected Variables from Employee SurveySurvey

Independent Variables (Job Satisfaction & Gender)

2. I am doing the kind of work

I want. Strongly Strongly

Disagree Agree

1 2 3 4 5 6 7 5. My job allows me to learn

new skills. Strongly Strongly

Disagree Agree 1 2 3 4 5 6 7

7. My work give me a sense ofaccomplishment. Strongly

Strongly Disagree Agree 1 2 3 4 5 6 7

19. Gender 0 = Male

1 = Female

Dependent Variable15. I am proud to tell others that I work for Samouel’s restaurant. Strongly Strongly

Disagree Agree 1 2 3 4 5 6 7

Using SPSS to Examine Dummy VariablesUsing SPSS to Examine Dummy Variables::

The SPSS click through sequence is: ANALYZE The SPSS click through sequence is: ANALYZE REGRESSION REGRESSION LINEAR. LINEAR. Go to Samouel’s employee Go to Samouel’s employee survey data andsurvey data and click on Xlick on X15 15 – Proud and move it to the – Proud and move it to the

Dependent Variables box. Click on XDependent Variables box. Click on X22, X, X55, X, X77 and X and X1919 and and

move them to the Independent Variables box. The box move them to the Independent Variables box. The box labeled “Method” has ENTER as the default and we will labeled “Method” has ENTER as the default and we will use it. Click on the “Statistics” button and use the use it. Click on the “Statistics” button and use the “Estimates” and “Model fit” defaults. Click on “Estimates” and “Model fit” defaults. Click on “Descriptives” then “Continue” and “OK” to run the “Descriptives” then “Continue” and “OK” to run the regression. regression.

Multiple Regression Assumptions:Multiple Regression Assumptions:

• Metrically measured variables.Metrically measured variables.

• Linearity.Linearity.

• Minimal multicollinearity among Minimal multicollinearity among

independent variables.independent variables.

• Constant variance of error terms (residuals).Constant variance of error terms (residuals).

• Independence of error terms.Independence of error terms.

• Normality of error term distribution.Normality of error term distribution.

Regression Analysis Regression Analysis TermsTerms

Explained variance = RExplained variance = R22 (coefficient of (coefficient of

determination).determination).

Unexplained variance = residuals (error).Unexplained variance = residuals (error).

Least Squares Regression Least Squares Regression LineLine

XX

Y

Y = averageY = average

Total DeviationTotal Deviation

Deviation not Deviation not explained by explained by regressionregression

Deviation Deviation explained by explained by regressionregression

Residuals PlotsResiduals Plots

Histogram of standardized residualsHistogram of standardized residuals – enables you to – enables you to

determine if the errors are normally distributed (see determine if the errors are normally distributed (see

Exhibit 1; also Hair pp. 174-5).Exhibit 1; also Hair pp. 174-5).

Normal probability plotNormal probability plot – enables you to determine if – enables you to determine if

the errors are normally distributed. It compares the the errors are normally distributed. It compares the

observed (sample) standardized residuals against the observed (sample) standardized residuals against the

expected standardized residuals from a normal expected standardized residuals from a normal

distribution (see Exhibit 2).distribution (see Exhibit 2).

ScatterPlot of residualsScatterPlot of residuals – can be used to test – can be used to test

regression assumptions. It compares the standardized regression assumptions. It compares the standardized

predicted values of the dependent variable against the predicted values of the dependent variable against the

standardized residuals from the regression equation standardized residuals from the regression equation

(see Exhibit 3). If the plot exhibits a random pattern (see Exhibit 3). If the plot exhibits a random pattern

then this indicates no identifiable violations of the then this indicates no identifiable violations of the

assumptions underlying regression analysis.assumptions underlying regression analysis.

Exhibit 1: Histogram of Employee Exhibit 1: Histogram of Employee Survey Dependent Variable XSurvey Dependent Variable X1515 – –

ProudProud

Regression Standardized Residual

2.25

2.00

1.75

1.50

1.25

1.00

.75

.50

.25

0.00

-.25

-.50

-.75

-1.00

-1.25

-1.50

-1.75

Histogram

Dependent Variable: X15 -- Proud

Fre

qu

en

cy

10

8

6

4

2

0

Std. Dev = .97

Mean = 0.00

N = 63.00

Exhibit 2: Normal Probability Plot of Exhibit 2: Normal Probability Plot of Regression Standardized ResidualsRegression Standardized Residuals

Normal P-P Plot of Regression Standardized Residual

Dependent Variable: X15 -- Proud

Observed Cum Prob

1.00.75.50.250.00

Exp

ecte

d C

um

Pro

b

1.00

.75

.50

.25

0.00

Normal probability plot = a graphical comparison of the shape of the sample distribution (observed) to the normal distribution. The straight line angled at 45 degrees is the normal distribution and the actual distribution (observed) is shown as deviations from the straight line.

Exhibit 3: Scatterplot of Employee Survey Exhibit 3: Scatterplot of Employee Survey Dependent Variable XDependent Variable X1515 – Proud – Proud

Scatterplot

Dependent Variable: X15 -- Proud

Regression Standardized Residual

3210-1-2

Re

gre

ssio

n S

tan

da

rdiz

ed

Pre

dic

ted

Va

lue

3

2

1

0

-1

-2

This is a scatterplot of the standardized residuals versus the predicted dependent (Y) values. If it exhibits a random pattern, which this plot does, then it indicates no identifiable violations of the assumptions underlying regression analysis and is called a “Null Plot”. See Hair, pp. 173-174.

Using SPSS to Examine ResidualsUsing SPSS to Examine Residuals::

SPSS includes several diagnostic tools to examine residuals. To run the SPSS includes several diagnostic tools to examine residuals. To run the regression that examines the residuals, first load the employee database. The click regression that examines the residuals, first load the employee database. The click through sequence is ANALYZE through sequence is ANALYZE REGRESSION REGRESSION LINEAR. Highlight X LINEAR. Highlight X1515 – Proud – Proud

and move it to the dependent variable box. Next highlight variables Xand move it to the dependent variable box. Next highlight variables X22, X, X55, X, X77, and X, and X1919

and move them to the independent variable box. ‘Enter’ is the default in the Methods and move them to the independent variable box. ‘Enter’ is the default in the Methods box and we will use it. Click on the Statistics button and ‘Estimates’ and ‘Model Fit’ box and we will use it. Click on the Statistics button and ‘Estimates’ and ‘Model Fit’ will be the defaults (if they are not defaults in your version of SPSS click them). Now, will be the defaults (if they are not defaults in your version of SPSS click them). Now, click on ‘Collinearity Diagnostics’ and then go to the bottom left of the screen in the click on ‘Collinearity Diagnostics’ and then go to the bottom left of the screen in the Residuals box and click on ‘Casewise Diagnostics’. The default is to identify outliers Residuals box and click on ‘Casewise Diagnostics’. The default is to identify outliers outside 3 standard deviations, but in this case we are going to be conservative and outside 3 standard deviations, but in this case we are going to be conservative and use 2 standard deviations. Click on Outliers outside and then place a 2 in the box for use 2 standard deviations. Click on Outliers outside and then place a 2 in the box for number of standard deviations. Next click on Continue. number of standard deviations. Next click on Continue.

This is the same sequence as earlier regression applications, but now we This is the same sequence as earlier regression applications, but now we also must go to the Plots button to request some new information. To produce plots also must go to the Plots button to request some new information. To produce plots of the residuals to check on potential violations of the regression assumptions, click of the residuals to check on potential violations of the regression assumptions, click on “ZPRED” and move it to the “Y” box. Then click on “ZRESID” and move it to the on “ZPRED” and move it to the “Y” box. Then click on “ZRESID” and move it to the “X” box. These two plots are for the Standardized Predicted Dependent Variable and “X” box. These two plots are for the Standardized Predicted Dependent Variable and Standardized Residuals. Next, click on Histogram and Normal Probability plot under Standardized Residuals. Next, click on Histogram and Normal Probability plot under the Standardized Residual Plots box on the lower left side of the screen. the Standardized Residual Plots box on the lower left side of the screen. Examination of these plots and tables enables us to determine whether the Examination of these plots and tables enables us to determine whether the hypothesized relationship between the dependent variable Xhypothesized relationship between the dependent variable X1515 and the independent and the independent

variables Xvariables X22, X, X55, X, X77, and X, and X1919 is linear, and also whether the error terms in the is linear, and also whether the error terms in the

regression model are normally distributed. Finally, click on ‘Continue’ and then on regression model are normally distributed. Finally, click on ‘Continue’ and then on ‘OK’ to run the program. The results are the same as in Exhibits 1 to 3.‘OK’ to run the program. The results are the same as in Exhibits 1 to 3.

DESCRIPTION OF DATABASE VARIABLESDESCRIPTION OF DATABASE VARIABLES

Variable Description Variable Description Variable TypeVariable Type

PERCEPTIONS OF HATCOPERCEPTIONS OF HATCOXX11 Delivery speedDelivery speed Metric Metric

XX22 Price levelPrice level Metric MetricXX33 Price flexibilityPrice flexibility Metric MetricXX44 Manufacturer’s imageManufacturer’s image Metric MetricXX55 Overall serviceOverall service Metric MetricXX66 Salesforce imageSalesforce image Metric MetricXX77 Product qualityProduct quality Metric Metric

PURCHASE OUTCOMESPURCHASE OUTCOMESXX99 Usage levelUsage level Metric MetricXX1010 Satisfaction levelSatisfaction level Metric Metric

PURCHASER CHARACTERISTICSPURCHASER CHARACTERISTICSXX88 Size of firmSize of firm Nonmetric NonmetricXX1111 Specification buyingSpecification buying Nonmetric NonmetricXX1212 Structure of procurementStructure of procurement Nonmetric NonmetricXX1313 Type of industryType of industry Nonmetric NonmetricXX1414 Type of buying situationType of buying situation Nonmetric Nonmetric

Variable Description Variable Type

Work Environment MeasuresX1 I am paid fairly for the work I do. MetricX2 I am doing the kind of work I want. MetricX3 My supervisor gives credit an praise for work well done. MetricX4 There is a lot of cooperation among the members of my work group. MetricX5 My job allows me to learn new skills. MetricX6 My supervisor recognizes my potential. MetricX7 My work gives me a sense of accomplishment. MetricX8 My immediate work group functions as a team. MetricX9 My pay reflects the effort I put into doing my work. MetricX10 My supervisor is friendly and helpful. MetricX11 The members of my work group have the skills and/or training

to do their job well. MetricX12 The benefits I receive are reasonable. MetricRelationship MeasuresX13 Loyalty – I have a sense of loyalty to Samouel’s restaurant. MetricX14 Effort – I am willing to put in a great deal of effort beyond that

expected to help Samouel’s restaurant to be successful. MetricX15 Proud – I am proud to tell others that I work for Samouel’s restaurant. MetricClassification VariablesX16 Intention to Search MetricX17 Length of Time an Employee NonmetricX18 Work Type = Part-Time vs. Full-Time NonmetricX19 Gender NonmetricX20 Age NonmetricX21 Performance Metric

Description of Employee Survey VariablesDescription of Employee Survey Variables

Variable Description Variable Type

Restaurant PerceptionsX1 Excellent Food Quality MetricX2 Attractive Interior MetricX3 Generous Portions MetricX4 Excellent Food Taste MetricX5 Good Value for the Money MetricX6 Friendly Employees MetricX7 Appears Clean & Neat MetricX8 Fun Place to Go MetricX9 Wide Variety of menu Items MetricX10 Reasonable Prices MetricX11 Courteous Employees MetricX12 Competent Employees MetricSelection Factor RankingsX13 Food Quality NonmetricX14 Atmosphere NonmetricX15 Prices NonmetricX16 Employees NonmetricRelationship VariablesX17 Satisfaction MetricX18 Likely to Return in Future MetricX19 Recommend to Friend MetricX20 Frequency of Patronage NonmetricX21 Length of Time a Customer NonmetricClassification VariablesX22 Gender NonmetricX23 Age NonmetricX24 Income NonmetricX25 Competitor NonmetricX26 Which AD Viewed (#1, 2 or 3) NonmetricX27 AD Rating MetricX28 Respondents that Viewed Ads Nonmetric

Description of Customer Survey VariablesDescription of Customer Survey VariablesVS.VS.