1 Chapter 17 Data Analysis: Investigation of Association © 2005 Thomson/South-Western

2 Figure 1: Scatter Diagrams of Sales vs. Marketing-Mix Variables Sales-Y ($000’s) TV Spots-X 1 Number of Salespersons-X 2 Sales-Y ($000’s)

3 Figure 1 continued Wholesaler Efficiency Index-X 3 Sales-Y ($000’s)

4 Figure 2: Relationship between Y and X 1 in the Probabilistic Model Y YiYi YiYi ^ eiei Y i = α 1 + β 1 X 1i ^ ^ ^ X 1i X1X1

5 Figure 3: Plot of Equation Relating Sales to TV Spots Sales ($000’s) TV Spots Y= X 1

6 Figure 4: Rectangular Distribution of Error Term Frequency Y X

7 Figure 5: Scatter of Points for Sample of n Observations X Y y x yiyi xixi P

8 Figure 6: Sample Scatter Diagrams and Their Correlation Coefficients A: r =.95B: r =.60 E: r = -.40 C: r = 1.00 F: r = -1.00D: r = -.60 I: r =.00H: r =.00G: r =.00

9 Figure 7: Hypothetical Relationship between Sales and TV Spots and between TV Spots and Number of Sales Representatives TV Spots Sales TV Spots Number of Salespersons

10 Territory Data for Click Ballpoint Pens Territory Sales (In Thousands) Y Advertising (TV Spots/Month) X 1 Number of Salespersons X 2 Wholesaler Efficiency Index X

11 Territory Data for Click Ballpoint Pens Territory Sales (In Thousands) Y Advertising (TV Spots/Month) X 1 Number of Salespersons X 2 Wholesaler Efficiency Index X

Sales vs. TV Spots Sales-Y Thousands of Dollars TV Spots-X 1

13 Sales vs. Number of Salespersons Sales-Y Thousands of Dollars Number of Salespersons-X 2

14 Sales vs. Wholesaler Efficiency Index Sales-Y Thousands of Dollars Wholesaler Efficiency Index-X 3

15 Computer Output of Regression of Sales Versus TV Spots Coefficient of Multiple Determination Coefficient of Multiple Correlation Standard Error of Estimate Constant TV Spots in Analysis of Variance Summary Table Due to Regression Due to Residuals Total Sum of Squares Degrees of Freedom Mean Square F Ratio Sales Dependent Variable Variable Regression Standard T- F- Partial Standardized Status Coefficient Error Value Level Correlation Coefficient

16 Plot of Equation Relating Sales to TV Spots Sales Thousands of Dollars TV Spots Y= X 1

17 Computer Output of Sales Versus TV Spots and Number of Salespersons Coefficient of Multiple Determination Coefficient of Multiple Correlation Standard Error of Estimate Variable Regression Standard T- F- Partial Standardized Status Coefficient Error Value Level Correlation Coefficient Constant TV Spots Analysis of Variance Summary Table Due to Regression Due to Residuals Total Sum of Squares Degrees of Freedom Mean Square F Ratio Sales Salespersons Dependent Variable

18 Computer Output of Sales Versus TV Spots, Number of Salespersons and Wholesaler Efficiency Coefficient of Multiple Determination Coefficient of Multiple Correlation Standard Error of Estimate Variable Regression Standard T- F- Partial Standardized Status Coefficient Error Value Level Correlation Coefficient Constant TV Spots Analysis of Variance Summary Table Due to Regression Due to Residuals Total Sum of Squares Degrees of Freedom Mean Square F Ratio Salespersons Wholeeff Sales Dependent Variable

19 Computer Output of Sales Versus TV Spots, # of Salespersons and Wholesaler Efficiency with Wholesaler Efficiency Expressed as a Dummy Variable Coefficient of Multiple Determination Coefficient of Multiple Correlation Standard Error of Estimate Constant TV Spots Analysis of Variance Summary Table Due to Regression Due to Residuals Total Sum of Squares Degrees of Freedom Mean Square F Ratio Sales Salespersons Fairdist Excldist Gooddist Dependent Variable Variable Regression Standard T- F- Partial Standardized Status Coefficient Error Value Level Correlation Coefficient

20 Hypothetical Relationship Between Sales and TV Spots, & Between TV Spots and #of Salespersons TV Spots TV Spots Number of Salespersons Sales

21  Measure of Linear Association between 2 Variables  Range:-1.00 < r xy < 1.00 Correlation Coefficient

22 y x r xy =-1.00 y x r xy =-.20 y x r xy =-.70 Relationship Between Scatterplots and Correlation Coefficients

23 y x r xy =.00 Nonlinear Relationship in the Data? “r” will be an approximation.

24 Effect of Multicollinearity

25 Predictions “Experts are sure the Dow will either rise or decline.” ‘Boy, business forecasting is an exact science, isn’t it?’ (Headlines, compiled by Jay Leno) A safe prediction for the market is the time of the closing bell. (101 Corporate Haiku, W. Warriner)

26  Representation of Categorical Variables for Regressions  Ex/ Favorability rating of Auto prototype as function of: age, gender, nationality –X1=age –X2=gender: M=1, W=0 –X3=nationality: 1=Asian, 2=European, 3=U.S.  #dummy variables required = # categories -1  Use X3 and define: –If X3=1 then DV1=1, else DV1=0 –If X3=2 then DV2=1, else DV2=0 Dummy Variables Nationality X3 DV1 DV2 Asian110 European201 U.S.300

27 Source: Conjoint Measurement Understand how consumers make trade-offs Discover attributes most valued by consumers Implications of attribute values, combinations for product design

28 Respondent’s Ordering of Various Product Descriptions Source: Capacity Price 4 Cup $28 $32 $38 8 Cup $28 $32 $38 22 Cup $28 $32 $38 Brewing Time 3 Minutes 6 Minutes 9 Minutes 12 Minutes

29 Some Attribute Utility Values & the Resulting Utilities for the Alternatives Under an Additive Rule Capacity Price 4 Cup $28 $32 $38 8 Cup $28 $32 $38 22 Cup $28 $32 $38 Brewing Time 3 Minutes 6 Minutes 9 Minutes 12 Minutes CapacityBrewing TimePrice 4 Cup.2 8 Cup.3 10 Cup.5 $28.6 $32.3 $ Minutes.5 6 Minutes.3 9 Minutes.1 12 Minutes.1

30 Plot of Input Ranks Versus Derived Cell Values Input Ranks Derived Cell Values

31 Figure 1: Key Decisions when Conducting a Conjoint Analysis Select Attributes Determine Attribute Levels Select Form of Presentation of Stimuli and Nature of Judgments to Be Secured from Subjects Decide on Whether, and If Yes How, Judgments Will Be Aggregated Determine Attribute Combinations to Be Used Select Analysis Technique

32 Coke store brand $1.99 $2.99 Coke store $1.99 $ Coke store $1.99 $ Which consumer is price sensitive, and which values quality or brand names?: Using Conjoint to Determine Price Sensitivity and Brand Equity

33 Figure 2: Pair-wise Approach to Data Collection in Conjoint Analysis $28 $32 $ Price Capacity (cups) Brewing Time (mins) Capacity (cups) $28 $32 $38 Brewing Time (mins) Price

34 Figure 3: Computer Administered Paired Comparison Choice Which would you prefer? Use the scale below to indicate your preference. 4-cup capacity 8-cup capacity 9-min.brewing time 3-min.brewing time $28 $38 Strongly Prefer Prefer Left Right