Chapter Fourteen 14-1. Statistical Analysis Procedures Statistical procedures that simultaneously analyze multiple measurements on each individual or

Chapter Fourteen

14-1

Statistical Analysis Procedures

Statistical procedures that simultaneously analyze multiple measurements on each individual or object under study.

14-2Key Terms & Definitions

Statistical Analysis


Correlation Analysis

Bivariate Techniques:

• Statistical methods of analyzing the relationship between variables.

Independent Variable:

• Variable believed to affect the value of the dependent variable.


Dependent Variable:

• Variable expected to be explained or caused by the independent variable.

Regression Analysis:

• The analysis of the strength of the linear relationship between variables when one is considered the independent variable and the other is the dependent variable.





The Strength of Association:

The coefficient of determination (R2): the percentage of the total variation in the dependent variable explained by the independent variable.

Pearson Correlation:

Analysis of the degree to which changes in one variable are associated with changes in another for use with metric data.

Measures of AssociationThe Concepts


Multiple Regression Key Concepts

Coefficient of Determination:

• Measured changes in the dependent and independent variables.

Regression Coefficients:

• Effect of the independent variable on the dependent variable.

Dummy Variables:

• Nominally scaled variables included in regression analysis.

A procedure for predicting the level or magnitude of a (metric) dependent variable based on the levels of multiple independent variables.


Regression Analysis


Regression Analysis


Uses of Regression Analysis


Coefficient of Determination:

Measure of the percentage of the variation in the dependent variable explained by variations in the independent variables.

Regression Coefficients:

Estimates of the effect of individual independent variables on the dependent variable.

Dummy Variables:

In regression analysis, a way of representing two-group or dichotomous, nominally scaled independent variables by coding one group as 0 and the other as 1.


Regression Analysis Measurement Applications

Potential Use and Interpretation Problems

Collinearity:

Correlation of independent variables with each other, which can bias estimates of regression coefficients.

Causation:

Inference that a change in one variable is responsible for (caused) an observed change in another variable.

Scaling of Coefficients:

A method of directly comparing the magnitudes of the regression coefficients of independent variables by scaling them in the same units or by standardizing the data.


Standardization Process


Cluster AnalysisThe general term for statistical procedures that classify objects, or people, into some number of mutually exclusive and exhaustive groups on the basis of two or more classification variables.


Consumers who frequently eat out but seldom eat at fast-food restaurants.

People who frequently eat out and also frequently eat at fast-food restaurants.

People who do not frequently eat out or frequently eat at fast-food restaurants.

Cluster AnalysisClustering people according to how frequently and where they eat out is a way of identifying a particular consumer base. An upscale restaurant can see where its customers fall.


Factor Analysis

A procedure for simplifying data by reducing a large set of variables to a smaller set of factors of composite variables by identifying dimensions of the data.

Factor: A linear combination of variables that are correlated with each other.


Factor Scores

In factor analysis, a factor score is calculated on each factor for each subject in the data set. For example, in a factor analysis with two factors, the following equations might be used to determine factor scores:


Factor Loading

Correlation between factor scores and the original variables.

Other Key Issues:

• Naming Factors• Number of factors to Retain


Factor Loading

Naming Factors

This is a somewhat subjective step. Usually a certain consistency exists among the variables that load highly on a given factor. For example, it is not surprising to see ratings “smooth ride” and “quiet ride” on the same factor.

Number of Factors to Retain

How many factors o you retain? A general rule of thumb is to stop

factoring when additional factors no longer make sense.


Conjoint AnalysisConjoint analysis could be used by a manufacturer of golf balls to determine the three most important features of a

golf ball and to see which ball meets the most needs of both consumer and manufacturer.


Average driving distance• 10 yards more than the golfer’s average• Same as the golfer's average• 10 yards less than the golfer's average

Average ball life• 54 holes• 36 holes• 18 holes

Price Per Ball• $2.00• $2.50• $3.00

Conjoint AnalysisConjoint analysis could be used by a manufacturer of golf balls to determine the three most important features of a

golf ball and to see which ball meets the most needs of both consumer and manufacturer.


For potential purchasers, the ideal golf ball has these characteristics• Average driving distance – 10 yards above average• Average ball life – 54 holes• Price $2.00

For the manufacturer, which is based on cost, the ideal golf ball has these characteristics:• Average driving distance – 10 yards below average• Average ball life – 18 holes• Price - $3.00

Conjoint Analysis

Multivariate procedure used to quantify the value consumers associate with different levels of

product/service attributes or features.


Conjoint Analysis – Estimating Utilities

Utilities: The relative value of attribute levels determined through conjoint analysis.


Conjoint Analysis – Estimating Utilities

Utilities: The relative value of attribute levels determined through conjoint analysis.


After some pre-processing, the actual data

mining process includes four steps:

1. Clustering

2. Classification

3. Modeling

4. Application

Data Mining Process

Key Terms & Definitions14-26

Step One ClusteringDiscovering groups and structures in the data based on selected sets of variables.

Step Two ClassificationApplying the structure identified in the cluster analysis to another subset of data.

Data Mining Process


Step Three ModelingUse regression to model the relationship or predict subgroup membership. Seeking high predictive accuracy.

Step Four ApplicationPutting your actionable data to work.

Data Mining Process


14-29

Key Terms & Definitions

• Regression Analysis• Coefficient of Determination• Regression Coefficients• Dummy Variables• Collinearity• Causation• Scaling of Coefficients

Links and button are active when in “Slide Show Mode”Key Terms & Definitions

• Discriminant Coefficient• Cluster Analysis• Factor Analysis• Factor Scores• Factor Loading• Conjoint Analysis• Estimating Utilities

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Chapter Fourteen 14-1. Statistical Analysis Procedures Statistical procedures that simultaneously analyze multiple measurements on each individual or