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Unformatted text preview: Lecture 9 Survey Research & Design in Psychology James Neill, 2011 Multiple Linear Regression II & Analysis of Variance I 2 Overview 1. Multiple Linear Regression II 2. Analysis of Variance I Multiple Linear Regression II • Summary of MLR I • Partial correlations • Residual analysis • Interactions • Analysis of change 4 1. Howell (2009). Correlation & regression [Ch 9] 2. Howell (2009). Multiple regression [Ch 15; not 15.14 Logistic Regression] 3. Tabachnick & Fidell (2001). Standard & hierarchical regression in SPSS (includes example writeups) [Alternative chapter from eReserve] Readings  MLR As per previous lecture 5 Summary of MLR I • Check assumptions – LOM, N , Normality, Linearity, Homoscedasticity, Collinearity, MVOs, Residuals • Choose type – Standard, Hierarchical, Stepwise, Forward, Backward • Interpret – Overall ( R 2 , Changes in R 2 (if hierarchical)), Coefficients (Standardised & unstandardised), Partial correlations • Equation – If useful (e.g., is the study predictive?) 7 Partial correlations ( r p ): Examples • Does years of marriage (IV 1 ) predict marital satisfaction (DV) after number of children is controlled for (IV 2 )? • Does time management (IV 1 ) predict university student satisfaction (DV) after general life satisfaction is controlled for (IV 2 )? 8 Partial correlations ( r p ) in MLR • When interpreting MLR coefficients, compare the 0order and partial correlations for each IV in each model → draw a Venn diagram • Partial correlations will be equal to or smaller than the 0order correlations • If a partial correlation is the same as the 0order correlation, then the IV operates independently on the DV. 9 Partial correlations ( r p ) in MLR • To the extent that a partial correlation is smaller than the 0order correlation, then the IV's explanation of the DV is shared with other IVs. • An IV may have a sig. 0order correlation with the DV, but a non sig. partial correlation. This would indicate that there is nonsig. unique variance explained by the IV. 10 Semipartial correlations ( sr 2 ) in MLR • The sr 2 indicate the %s of variance in the DV which are uniquely explained by each IV. • In PASW, the sr s are labelled “part”. You need to square these to get sr 2 . • For more info, see Allen and Bennett (2008) p. 182 11 Part & partial correlations in SPSS In Linear Regression  Statistics dialog box, check “Part and partial correlations” 12 Coefficients a.521.460.325.178 Worry Ignore the Problem Model 1 Zeroorder Partial Correlations Dependent Variable: Psychological Distress a. Multiple linear regression  Example 13 .18 .32 .46 .52 .34 Y X 1 X 2 15 Residual analysis Three key assumptions can be tested using plots of residuals: 1. Linearity : IVs are linearly related to DV 2. Normality of residuals 3. Equal variances (Homoscedasticity) 16 Residual analysis Assumptions about residuals: • Random noise • Sometimes positive, sometimes negative but, on average, 0 • Normally distributed about 0 Residual analysis Residual analysis...
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