Overview
Upload a single MS-Word document with your answers.
Use all 200 observations of the HBAT_200.sav file.
Estimate the following relationship: X21 = b0 + b1X6 + b2X8 + b3X9 + b4X12
with the Statistics for Estimates, Model fit, Covariance matrix, & Collinearity Diagnostics
and Plots for all partial plots & Scatter of *SRESID on *ZPRED
1a. What is the R2 and Adjusted R2?
1b. What are the unstandardized coefficient estimates?
1c. Which coefficient estimates are statistically significant at the 5% level?
1d. What is the predicted value for X21 if X6=6, X8=7, X9=5, and X12=4?
1e. Do any of the coefficient estimates have a VIF factor that indicated multicollinearity is a problem? Which 2 variables have the highest (in absolute value) correlation with each other and what is that correlation? Does this correlation indicate that multicollinearity is a problem?
1f. Do any of the Studentized Residuals lie outside of the 1.96 to -1.96 range? If so, what observations are they?
1g. Consider the partial plot of X21 (y-axis) on X12 (x-axis). Does that look like a positive or a negative relationship? Explain.
For h and i, suppose you do not include X8 in the regression. That is you estimate: X21 = b0 + b1X6 + b2X9 + b3X12
1h. What happens to the Adjusted R2 if you do not include X8 in the regression?
1i. What is the predicted value for X21 if X6=6, X9=5, and X12=4?
1j. Do you think X8 should be included or excluded from the model? Explain in 50 words or less.
2) MANOVA
Use all 200 observations of the HBAT_200.sav file.
A Factorial Design with Two Independent Variables (X5: Distribution System, X4: Region)
Stage 1: Objective of the Analysis
Basic Research Questions Addressed Jointly:
- Is the direct distribution system more effective for customers in the USA?
- Do the two distribution systems show differences for customers outside of the USA?
- Is the direct distribution system always preferred over the indirect system across the regions of X4?
Examining Group Profiles
2a. Create and paste a Table similar to Table 6.9: Descriptive Statistics of Purchase Outcome Measures (X19, X20, and X21) for Groups of X4 (Region) by X5 (Distribution System)
Stage 2: Research Design of the MANOVA
2b. What are the Sample Sizes for USA/NA-Indirect? USA/NA-Direct? Outside NA-Indirect? Outside NA-Direct?
Stage 3: Assumptions in MANOVA
Independence of Observations: random sampling plan in the observational study
Normality of the Dependent Variables: see Example 1
Correlation of the Dependent Variables: see Example 1
2c. Create and paste a table similar to Table 6.11, Multivariate and Univariate Measures for Testing Homoscedasticity across Groups of X4 by X5
2d. Which variable has individual heteroscedasticity using alpha = 0.05?
2e. Can you conclude that the observed covariance matrices of the dependent variables are equal across all group using alpha = 0.05?
2f. Create and paste 3 boxplots similar to Figure 6.17 for X19/X20/X21 for groups of X5 by X4 (X4 on the X-Axis)
2g. What observations show up as outliers? Do they show up in all 3 charts consistently?
Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit
Assessing the Interaction Effect:
2h. Create and paste 3 figures similar to Figure 6.18, Graphical Displays of Interaction Effects (X4 on the X-Axis)
2i. Do any of the variable have non-parallel lines indicating an ordinal interaction effect?
Testing the Interaction and Main Effects
2j. Create and paste a table similar to Table 6.12: Multivariate and Univariate Tests
2k. Which variable is not statistical significance in either the multivariate and the univariate tests using alpha = 0.05?
Stage 5: Interpretation of the Results
2l. Which distribution channel is preferred Direct or Indirect?
2m. Is the magnitude of the preference larger in the USA/NA or Outside NA?