Multivariate Correlational Analysis: An Introduction
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1 Assignment. Multivariate Correlational Analysis: An Introduction Mertler & Vanetta, Chapter 7 Kachigan, Chapter 4, pps Terms you should know. Multiple Regression Linear Equations Least Squares Criterion Residual Regression Coefficient Beta weight Multiple Regression Techniques Standard or Simultaneous Rev. August, 2006 Page - 90 GradStat Study Guide
2 Stepwise Forward Stepwise Backward Stepwise Partial Correlation Multicollinearity Tolerance Cross-validation Canonical Correlation Canonical Variate Rev. August, 2006 Page - 91 GradStat Study Guide
3 Formulas and Symbols You Should Know. R R R 2 B $ 2 R /k 2 (1 R ) /(N k 1) Rev. August, 2006 Page - 92 GradStat Study Guide
4 Computations You Should be Able to Perform. The following are results from a validation study done by undergraduates. They were looking at the relationship between five scales in the Activity Vector Analysis (AVA) scales and the Recklessness scale taken from Cloninger s Temperance and Character Inventory. The five AVA scales are Assertiveness (V-1), Sociability (V-2), Calmness (V-3), Conformity (V-4), and Conscious Restraint (V-5). It was predicted that there would be a negative relationship between Calmness (V-3) and Recklessness. It was also thought that there would be a complex relationship between the AVA vectors but it was not known what this relationship would be. Table 1. Descriptive Statistics Mean Std. N Deviation Recklessness(1) SCV SCV SCV SCV SCV Table 2. Correlations Recklessness(1) SCV1 SCV2 SCV3 SCV4 SCV5 Recklessness(1) Correlation Sig. (1-tail) N SCV1 Correlation Sig. (1-tail) SCV2 Correlation Sig. (1-tailed) SCV3 Correlation Sig. (1-tail) SCV4 Correlation Sig. (1-tail) SCV5 Correlation Sig. (1-tail) Rev. August, 2006 Page - 93 GradStat Study Guide
5 Table 3. Model Summary, Stepwise Regression Model R R Square Adjusted R Square Std. Error of the Estimate a Predictors: (Constant), SCV3 b Predictors: (Constant), SCV3, SCV2 Coefficients Unstandardized Coefficients Standardized Coefficients t Sig. Model B Std. Beta Error 1 (Constant) SCV (Constant) SCV SCV a Dependent Variable: Recklessness(1) 1. How many people completed the AVA? 2. Which AVA variables are significantly correlated with Recklessness? 3. Was the basic research hypothesis supported? Why or why not? 4. Using eyeball statistics does there appear to be evidence for multicollinearity among the predictors? 5. What variable was selected in the first step of the stepwise regression? Why was this variable entered first? 6. What is R? 7. What variables were entered in the second step? 8. How much additional variability was added in the second step? 9. What is the standard error of R? Rev. August, 2006 Page - 94 GradStat Study Guide
6 Concepts and Interpretation. 1. What is meant by multicollinearity? What influence does it have on multiple regression analyses? 2. How can you detect multicollinearity? 3. How can you deal withy multicollinearity? 4. What assumptions are made about the data in a multiple regression analysis. 5. What can you learn from each of the following multiple regression techniques? a. Simultaneous b. Forward stepwise c. Backward stepwise Rev. August, 2006 Page - 95 GradStat Study Guide
7 SPSS Assignment #6. NAME: 1. Using SPSS, conduct the following: a. Calculate the correlation between age and the five AVA vectors using the C-Scores. i. What is the highest correlation? ii. What is the lowest correlation? iii. How do you interpret the correlation between age and Conscious Restraint? b. Calculate the multiple regression predicting V-5 from the other four vectors? i. Do a full regression. (1) What is R? ii. Do a stepwise regression. (1) What variable accounts for the most variance in this calculation? (2) What is the Beta weight for this variable? (3) What is the beta weight for this variable? (4) What is the standard error of estimate? (5) Do you think that you could make a fairly accurate prediction of V-5 from the other four vectors? Why or why not? Rev. August, 2006 Page - 96 GradStat Study Guide
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