Chapter Fifteen Overview of Other Multivariate Techniques and Data Mining

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Chapter Fifteen Overview of Other Multivariate Techniques and Data Mining Slide 2 Copyright Houghton Mifflin Company. All rights reserved.15 | 2 Dependence and Interdependence Techniques Dependence technique One variable is designated as the dependent variable and the rest are treated as independent variables Interdependence technique There are no dependent and independent variable designations, all variables are treated equally in a search for underlying patterns of relationships Slide 3 Copyright Houghton Mifflin Company. All rights reserved.15 | 3 Dependence Technique Regression Analysis Input Data Dependent variable(s) - metric Independent variable(s) - metric Primary Purpose of the Technique Ascertain the relative importance of independent variable(s) in explaining variation in the dependent variable Predict dependentvariable values for given values of the independent variable(s) Slide 4 Copyright Houghton Mifflin Company. All rights reserved.15 | 4 Table 15.1 Overview of Multivariate Techniques Slide 5 Copyright Houghton Mifflin Company. All rights reserved.15 | 5 Analysis of Variance ANOVA is appropriate in situations where the independent variable is set at certain specific levels (called treatments in an ANOVA context) and metric measurements of the dependent variable are obtained at each of those levels Slide 6 Copyright Houghton Mifflin Company. All rights reserved.15 | 6 Example 24 Stores Chosen randomly for the study 8 Stores randomly chosen for each treatment Treatment 1 Store brand sold at the regular price Treatment 2 Store brand sold at 50 off the regular price Treatment 3 Store brand sold at 75 off the regular price monitor sales of the store brand for a week in each store Slide 7 Copyright Houghton Mifflin Company. All rights reserved.15 | 7 Table 15.2 Unit Sales Data Under Three Pricing Treatments Slide 8 Copyright Houghton Mifflin Company. All rights reserved.15 | 8 EG1 -- Experiment Group 1, X1-- Regular Price EG2 -- Experiment Group 2, X2-- 50c off EG3 -- Experiment Group 3, X3-- 75c off O1 -- Observation (monitoring unit sales data in each store) O2 -- Observation (monitoring unit sales data in each store) O3 -- Observation (monitoring unit sales data in each store) After Only Design Slide 9 Copyright Houghton Mifflin Company. All rights reserved.15 | 9 EG 1 (R)X 1 O 1 EG 2 (R)X 2 O 2 EG 3 (R)X 3 O 3 After Only Design EG1 -- Experiment Group 1, X1-- Regular Price EG2 -- Experiment Group 2, X2-- 50c off EG3 -- Experiment Group 3, X3-- 75c off O1 -- Observation (monitoring unit sales data in each store) O2 -- Observation (monitoring unit sales data in each store) O3 -- Observation (monitoring unit sales data in each store) Slide 10 Copyright Houghton Mifflin Company. All rights reserved.15 | 10 ANOVA Grocery Store Hypothesis Grocery Store Example H o 1 = 2 = 3 H a At least one is different from one or more of the others Hypotheses for K Treatment groups or samples H o 1 = 2 =... = k H a At least one is different from one or more of the others Slide 11 Copyright Houghton Mifflin Company. All rights reserved.15 | 11 Exhibit 15.1 SPSS Computer Output for ANOVA Analysis Slide 12 Copyright Houghton Mifflin Company. All rights reserved.15 | 12 Bank Customers Gender MaleFemale < 35 Years 35-64 Years > 64 Years < 35 Years 35-64 Years > 64 Years Measure Overall Perceptions Bank Customer Perceptions Study Slide 13 Copyright Houghton Mifflin Company. All rights reserved.15 | 13 Tests Between-Subjects Effects Dependent Variable:Overall Quality of the Companys Services a. R Squared =.824 (Adjusted R Squared =.822) Bank Customer Perceptions Study (Contd) Slide 14 Copyright Houghton Mifflin Company. All rights reserved.15 | 14 Bank Customer Perceptions Study (Contd) Male and female customers differed in their overall perceptions Customers' perceptions differed according to their ages Slide 15 Copyright Houghton Mifflin Company. All rights reserved.15 | 15 Sex and age interacted in influencing perceptions Bank Customer Perceptions Study (Contd) Slide 16 Copyright Houghton Mifflin Company. All rights reserved.15 | 16 Factorial Anova The Factorial ANOVA is used to analyze data from a factorial design experiment variable Using the grocery store example Add in the impact of an in-store, point of purchase display on orange juice In addition to the pricing factor Slide 17 Copyright Houghton Mifflin Company. All rights reserved.15 | 17 Exhibit 15.2 Illustrations of Main and Interaction Effects Slide 18 Copyright Houghton Mifflin Company. All rights reserved.15 | 18 Factorial ANOVA The interaction effect is calculated and F- tested SS T =SS TR + SS E = SS A + SS B + SS AB + SS E SS A = Effect of Treatment A SS B = Effect of Treatment B SS AB = Interaction Effect Slide 19 Copyright Houghton Mifflin Company. All rights reserved.15 | 19 Discriminant Analysis Identifies the distinguishing features of prespecified subgroups of units that are formed on the basis of some dependent variable Examples of subgroups Heavy, moderate, and light users of a product Homeowners and renters Viewers and nonviewers of a television program Slide 20 Copyright Houghton Mifflin Company. All rights reserved.15 | 20 Discriminant Analysis (Contd) Dependent Variable Categorical: as many categories as there are subgroups Heavy, moderate, and light users: 3 categories Independent Variable Metric-scaled Purpose of discriminant analysis is to classify new units into one of the subgroups given the new units values of the independent variable Slide 21 Copyright Houghton Mifflin Company. All rights reserved.15 | 21 Example Computer Manufacturer Household income Number of years of formal education PC OwnershipNot Owning A PC Slide 22 Copyright Houghton Mifflin Company. All rights reserved.15 | 22 Exhibit 15.3 Scatter Plot of Income and Education Data for Personal Computer Owners and Nonowners Slide 23 Copyright Houghton Mifflin Company. All rights reserved.15 | 23 Using the Discriminant Function Y = v 1 X 1 + v 2 X 2 Discriminant weights v 1 and v 2 can be interpreted as signifying the relative importance of X 1 and X 2 in being able to discriminate between the two groups Ynew = v 1 X 1, new + v 2 X 2, new The program assigns either to the owner group or to the non-owner group based on the criterion value Slide 24 Copyright Houghton Mifflin Company. All rights reserved.15 | 24 Evaluating a Discriminant Function Confusion Matrix Indicates the degree of correspondence, or lack thereof, between the actual groupings of the sample units and the predicted groupings obtained by classifying the same units through the discriminant function Slide 25 Copyright Houghton Mifflin Company. All rights reserved.15 | 25 Table 15.3 Confusion Matrix Slide 26 Copyright Houghton Mifflin Company. All rights reserved.15 | 26 Usefulness of Discriminant Analysis Discriminant analysis is very useful for Defining customer segments Identifying critical characteristics capable of distinguishing among them Classifying prospective customers into appropriate segments Slide 27 Copyright Houghton Mifflin Company. All rights reserved.15 | 27 Factor Analysis A data and variable reduction technique that attempts to partition a given set of variables into groups of maximally correlated variables Slide 28 Copyright Houghton Mifflin Company. All rights reserved.15 | 28 Intuitive Explanation Consider two statements from the Star Brand Inc.(SBI) survey S 1. I have been satisfied with the Star products I have purchased S 2. When I have to purchase a home appliance in the future, it will likely be a Star product Slide 29 Copyright Houghton Mifflin Company. All rights reserved.15 | 29 Exhibit 15.6 Situation in Which Factor Analysis Will Be Beneficial: S1 and S2 Highly Correlated Slide 30 Copyright Houghton Mifflin Company. All rights reserved.15 | 30 Exhibit 15.7 Situation in Which Factor Analysis Will Not Be Beneficial: S1 and S2 Poorly Correlated Slide 31 Copyright Houghton Mifflin Company. All rights reserved.15 | 31 Factor Analysis Output and Its Interpretation Primary output of factor analysis is a factor- loading matrix Achieved Communality represents the proportion of variance in an original variable accounted for by all the extracted factors. Each original variable will have an achieved communality value in the factor analysis output Slide 32 Copyright Houghton Mifflin Company. All rights reserved.15 | 32 Factor Analysis Output (cont) The eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor. Note that the eigenvalue is not the percent of variance explained but the amount of variance in relation to total variance (since variables are standardized to have means of 0 and variances of 1, total variance is equal to the number of variables). SPSS will output a corresponding column titled '% of variance'. A factor's eigenvalue may be computed as the sum of its squared factor loadings for all the variables. Slide 33 Copyright Houghton Mifflin Company. All rights reserved.15 | 33 Table 15.4 Factor-Loading Matrix Based on Data from Study of Star Customers Slide 34 Copyright Houghton Mifflin Company. All rights reserved.15 | 34 Reducing Star Data X 1, X 4, and X 6 can be combined into one factor X 2, X 3, and X 5 can be into a second factor 6 variables can be reduced to two factors Slide 35 Copyright Houghton Mifflin Company. All rights reserved.15 | 35 Potential Applications of Factor Analysis Used to Develop concise but comprehensive, multiple- item scales for measuring various marketing constructs Illuminate the nature of distinct dimensions underlying an existing data set Convert a large volume of data into a set of factor scores on a limited number of uncorrelated factors Slide 36 Copyright Houghton Mifflin Company. All rights reserved.15 | 36 Cluster Analysis Segment objects into groups so that members within each group a