Podcast
Questions and Answers
What is the purpose of standard regression?
What is the purpose of standard regression?
What is the best-fitting line in regression analysis?
What is the best-fitting line in regression analysis?
What is the definition of error in regression analysis?
What is the definition of error in regression analysis?
What is unique variance in multiple regression?
What is unique variance in multiple regression?
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What is the concept of shared variance in multiple regression?
What is the concept of shared variance in multiple regression?
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What is the general linear model in regression and ANOVA?
What is the general linear model in regression and ANOVA?
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What is the standardised slope in regression analysis?
What is the standardised slope in regression analysis?
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What is the regression coefficient R2?
What is the regression coefficient R2?
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What is the primary purpose of using partial correlation?
What is the primary purpose of using partial correlation?
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What is the primary difference between a mediated regression model and a hierarchical regression model?
What is the primary difference between a mediated regression model and a hierarchical regression model?
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What is the primary purpose of using tolerance and variance inflation factor (VIF)?
What is the primary purpose of using tolerance and variance inflation factor (VIF)?
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What is the primary assumption of the standard multiple regression model?
What is the primary assumption of the standard multiple regression model?
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What is the primary purpose of using bootstrapping in mediated regression?
What is the primary purpose of using bootstrapping in mediated regression?
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What is the primary purpose of including a covariate in an analysis?
What is the primary purpose of including a covariate in an analysis?
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What is the primary difference between a moderated regression model and an additive model?
What is the primary difference between a moderated regression model and an additive model?
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What does an omnibus test assess in ANOVA?
What does an omnibus test assess in ANOVA?
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What is the primary purpose of using the Johnson-Neyman test?
What is the primary purpose of using the Johnson-Neyman test?
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What is the primary assumption of homogeneity of regression?
What is the primary assumption of homogeneity of regression?
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What is the primary difference between a bivariate correlation and a semi-partial correlation?
What is the primary difference between a bivariate correlation and a semi-partial correlation?
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What is the primary purpose of using a pick-a-point technique in moderated regression?
What is the primary purpose of using a pick-a-point technique in moderated regression?
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What is the purpose of Cook's Distance?
What is the purpose of Cook's Distance?
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What is the primary issue in moderated regression?
What is the primary issue in moderated regression?
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What is the primary advantage of using bootstrapping in mediated regression?
What is the primary advantage of using bootstrapping in mediated regression?
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What is the purpose of rotating a factor matrix?
What is the purpose of rotating a factor matrix?
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What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
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What is the assumption of homogeneity of regression in ANCOVA?
What is the assumption of homogeneity of regression in ANCOVA?
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What is the main effect in ANOVA?
What is the main effect in ANOVA?
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What is a studentized residual in regression analysis?
What is a studentized residual in regression analysis?
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What is the assumption in ANOVA when the association between the covariate and the dependent variable is the same for each group?
What is the assumption in ANOVA when the association between the covariate and the dependent variable is the same for each group?
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What type of effect does an unconditional effect in regression analysis represent?
What type of effect does an unconditional effect in regression analysis represent?
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What is a characteristic of a balanced design in ANOVA?
What is a characteristic of a balanced design in ANOVA?
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What is the purpose of Mauchly's test in a study?
What is the purpose of Mauchly's test in a study?
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What does a KMO sampling technique measure in FA/PCA?
What does a KMO sampling technique measure in FA/PCA?
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What is the purpose of Bartlett's test of sphericity in FA/PCA?
What is the purpose of Bartlett's test of sphericity in FA/PCA?
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What is a consequence of an unbalanced design in ANOVA?
What is a consequence of an unbalanced design in ANOVA?
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When is Mauchly's test not conducted in a study?
When is Mauchly's test not conducted in a study?
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What is the primary purpose of using partial correlation?
What is the primary purpose of using partial correlation?
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What does a discrepancy score indicate?
What does a discrepancy score indicate?
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What is the primary purpose of the general linear model in regression and ANOVA?
What is the primary purpose of the general linear model in regression and ANOVA?
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What is the assumption of homoscedasticity?
What is the assumption of homoscedasticity?
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What does the standardised slope represent in regression analysis?
What does the standardised slope represent in regression analysis?
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What is multicollinearity?
What is multicollinearity?
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What is the primary purpose of using hierarchical regression?
What is the primary purpose of using hierarchical regression?
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What is the difference between unique variance and shared variance in multiple regression?
What is the difference between unique variance and shared variance in multiple regression?
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What is the primary difference between a mediated regression model and a hierarchical regression model?
What is the primary difference between a mediated regression model and a hierarchical regression model?
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What is the purpose of the regression coefficient R2 in regression analysis?
What is the purpose of the regression coefficient R2 in regression analysis?
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What is the difference between the unstandardised coefficient and the standardised coefficient in regression analysis?
What is the difference between the unstandardised coefficient and the standardised coefficient in regression analysis?
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What is the purpose of using the Sobel test?
What is the purpose of using the Sobel test?
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What is the purpose of SS regression in regression analysis?
What is the purpose of SS regression in regression analysis?
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What is the primary purpose of using moderated regression analysis?
What is the primary purpose of using moderated regression analysis?
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What is the primary purpose of using the Johnson-Neyman test?
What is the primary purpose of using the Johnson-Neyman test?
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What is the difference between SS total and SS residual in regression analysis?
What is the difference between SS total and SS residual in regression analysis?
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What is the purpose of semi-partial correlation in regression analysis?
What is the purpose of semi-partial correlation in regression analysis?
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What is the primary difference between conditional and unconditional effects in regression analysis?
What is the primary difference between conditional and unconditional effects in regression analysis?
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What is the main consequence of an unbalanced design in ANOVA?
What is the main consequence of an unbalanced design in ANOVA?
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What is the primary purpose of Mauchly's test in a study?
What is the primary purpose of Mauchly's test in a study?
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What is the primary purpose of the KMO sampling technique in FA/PCA?
What is the primary purpose of the KMO sampling technique in FA/PCA?
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What is the primary purpose of Bartlett's test of sphericity in FA/PCA?
What is the primary purpose of Bartlett's test of sphericity in FA/PCA?
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What is a characteristic of a balanced design in ANOVA?
What is a characteristic of a balanced design in ANOVA?
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What is the primary difference between a conditional and an unconditional effect in ANOVA?
What is the primary difference between a conditional and an unconditional effect in ANOVA?
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When is Mauchly's test not conducted in a study?
When is Mauchly's test not conducted in a study?
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What is the primary requirement for a covariate to be included in an analysis?
What is the primary requirement for a covariate to be included in an analysis?
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What is the primary purpose of using a semi-partial correlation?
What is the primary purpose of using a semi-partial correlation?
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What is the primary difference between a between-subjects and a within-subjects design in ANOVA?
What is the primary difference between a between-subjects and a within-subjects design in ANOVA?
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What is the primary purpose of using bootstrapping in mediated regression?
What is the primary purpose of using bootstrapping in mediated regression?
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What is the primary assumption of homogeneity of regression in ANCOVA?
What is the primary assumption of homogeneity of regression in ANCOVA?
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What is the primary purpose of rotating a factor matrix?
What is the primary purpose of rotating a factor matrix?
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What is the primary purpose of using Cook's Distance?
What is the primary purpose of using Cook's Distance?
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What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
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What is the primary difference between an omnibus test and a main effect in ANOVA?
What is the primary difference between an omnibus test and a main effect in ANOVA?
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What is the primary purpose of using an F statistic in ANOVA?
What is the primary purpose of using an F statistic in ANOVA?
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In a partial correlation, what is removed from the predictor variable?
In a partial correlation, what is removed from the predictor variable?
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What is the primary assumption of the standard multiple regression model?
What is the primary assumption of the standard multiple regression model?
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What is the purpose of using tolerance and variance inflation factor (VIF) in regression analysis?
What is the purpose of using tolerance and variance inflation factor (VIF) in regression analysis?
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What is the primary purpose of using mediated regression analysis?
What is the primary purpose of using mediated regression analysis?
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What is the primary advantage of using bootstrapping in mediated regression?
What is the primary advantage of using bootstrapping in mediated regression?
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What is the primary purpose of using moderated regression analysis?
What is the primary purpose of using moderated regression analysis?
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What is the primary difference between an interactive model and an additive model?
What is the primary difference between an interactive model and an additive model?
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What is the primary purpose of using a pick-a-point technique in moderated regression?
What is the primary purpose of using a pick-a-point technique in moderated regression?
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What is the primary assumption of homogeneity of regression?
What is the primary assumption of homogeneity of regression?
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What is the primary purpose of the general linear model in regression and ANOVA?
What is the primary purpose of the general linear model in regression and ANOVA?
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What is the primary issue in moderated regression?
What is the primary issue in moderated regression?
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Which of the following statements is true about the standardized slope in regression analysis?
Which of the following statements is true about the standardized slope in regression analysis?
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What is the difference between unique variance and shared variance in multiple regression?
What is the difference between unique variance and shared variance in multiple regression?
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What is the purpose of the regression coefficient R2 in regression analysis?
What is the purpose of the regression coefficient R2 in regression analysis?
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What is the difference between the unstandardized coefficient and the standardized coefficient in regression analysis?
What is the difference between the unstandardized coefficient and the standardized coefficient in regression analysis?
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What is the primary purpose of using a covariate in an analysis?
What is the primary purpose of using a covariate in an analysis?
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What is the primary purpose of SS regression in regression analysis?
What is the primary purpose of SS regression in regression analysis?
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What is the difference between a bivariate correlation and a semi-partial correlation?
What is the difference between a bivariate correlation and a semi-partial correlation?
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What is the purpose of the total variance SS total in regression analysis?
What is the purpose of the total variance SS total in regression analysis?
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What is the assumption of homogeneity of regression in ANCOVA?
What is the assumption of homogeneity of regression in ANCOVA?
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What is the primary purpose of semi-partial correlation in regression analysis?
What is the primary purpose of semi-partial correlation in regression analysis?
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What is the primary purpose of using bootstrapping in mediated regression?
What is the primary purpose of using bootstrapping in mediated regression?
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What is the difference between a main effect and a simple effect in ANOVA?
What is the difference between a main effect and a simple effect in ANOVA?
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What is Cook's Distance?
What is Cook's Distance?
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What is the primary purpose of rotating a factor matrix?
What is the primary purpose of rotating a factor matrix?
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What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
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What is a studentized residual?
What is a studentized residual?
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What is an omnibus test?
What is an omnibus test?
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What is the primary difference between conditional and unconditional effects in ANOVA or regression?
What is the primary difference between conditional and unconditional effects in ANOVA or regression?
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What is the primary consequence of an unbalanced design in ANOVA?
What is the primary consequence of an unbalanced design in ANOVA?
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What is the purpose of Mauchly's test in a study?
What is the purpose of Mauchly's test in a study?
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What is the primary purpose of the KMO sampling technique in FA/PCA?
What is the primary purpose of the KMO sampling technique in FA/PCA?
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What is the primary purpose of Bartlett's test of sphericity in FA/PCA?
What is the primary purpose of Bartlett's test of sphericity in FA/PCA?
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When is Mauchly's test not conducted in a study?
When is Mauchly's test not conducted in a study?
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What is the primary difference between a balanced and unbalanced design in ANOVA?
What is the primary difference between a balanced and unbalanced design in ANOVA?
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What is the primary purpose of using conditional effects in ANOVA or regression?
What is the primary purpose of using conditional effects in ANOVA or regression?
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What is the primary concept that standard regression predicts?
What is the primary concept that standard regression predicts?
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What is the term for the difference between the observed value and the true value in regression analysis?
What is the term for the difference between the observed value and the true value in regression analysis?
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What is the range of the regression coefficient R2?
What is the range of the regression coefficient R2?
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What is the purpose of SS regression in regression analysis?
What is the purpose of SS regression in regression analysis?
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What is the standardised slope in regression analysis?
What is the standardised slope in regression analysis?
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What is the difference between unique variance and shared variance in multiple regression?
What is the difference between unique variance and shared variance in multiple regression?
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What is the general linear model in regression and ANOVA?
What is the general linear model in regression and ANOVA?
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What is the difference between the unstandardised coefficient and the standardised coefficient in regression analysis?
What is the difference between the unstandardised coefficient and the standardised coefficient in regression analysis?
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What is the primary purpose of using partial correlation?
What is the primary purpose of using partial correlation?
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What is the assumption of homoscedasticity in regression analysis?
What is the assumption of homoscedasticity in regression analysis?
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What is the primary purpose of using tolerance and variance inflation factor (VIF) in regression analysis?
What is the primary purpose of using tolerance and variance inflation factor (VIF) in regression analysis?
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What is the difference between an interactive model and an additive model in moderated regression?
What is the difference between an interactive model and an additive model in moderated regression?
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What is the primary difference between conditional and unconditional effects in ANOVA or regression?
What is the primary difference between conditional and unconditional effects in ANOVA or regression?
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What is the primary purpose of using a pick-a-point technique in moderated regression?
What is the primary purpose of using a pick-a-point technique in moderated regression?
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What is the primary consequence of an unbalanced design in ANOVA?
What is the primary consequence of an unbalanced design in ANOVA?
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What is the primary issue in moderated regression?
What is the primary issue in moderated regression?
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What is the primary purpose of Mauchly's test?
What is the primary purpose of Mauchly's test?
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What is the primary purpose of using bootstrapping in mediated regression?
What is the primary purpose of using bootstrapping in mediated regression?
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What is the primary purpose of the KMO sampling technique in FA/PCA?
What is the primary purpose of the KMO sampling technique in FA/PCA?
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What is the primary difference between a mediated regression model and a hierarchical regression model?
What is the primary difference between a mediated regression model and a hierarchical regression model?
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What is the primary purpose of using moderated regression analysis?
What is the primary purpose of using moderated regression analysis?
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What is the primary purpose of Bartlett's test of sphericity?
What is the primary purpose of Bartlett's test of sphericity?
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What is the assumption of normality in regression analysis?
What is the assumption of normality in regression analysis?
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What is the primary difference between a balanced and unbalanced design in ANOVA?
What is the primary difference between a balanced and unbalanced design in ANOVA?
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When is Mauchly's test not conducted in a study?
When is Mauchly's test not conducted in a study?
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What is the primary assumption of ANOVA when the association between the covariate and the DV is the same for each group?
What is the primary assumption of ANOVA when the association between the covariate and the DV is the same for each group?
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What is the primary assumption for using an ANCOVA?
What is the primary assumption for using an ANCOVA?
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What is the main difference between a bivariate correlation and a semi-partial correlation?
What is the main difference between a bivariate correlation and a semi-partial correlation?
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What is the purpose of using a rotation in a factor matrix?
What is the purpose of using a rotation in a factor matrix?
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What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
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What is the purpose of Cook's Distance?
What is the purpose of Cook's Distance?
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What is the primary purpose of using bootstrapping in mediated regression?
What is the primary purpose of using bootstrapping in mediated regression?
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What is the main difference between a disordinal interaction and a ordinal interaction?
What is the main difference between a disordinal interaction and a ordinal interaction?
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What is the primary purpose of using an omnibus test in ANOVA?
What is the primary purpose of using an omnibus test in ANOVA?
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What is the primary purpose of using a covariate in an analysis?
What is the primary purpose of using a covariate in an analysis?
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What is the assumption of homogeneity of regression in ANCOVA?
What is the assumption of homogeneity of regression in ANCOVA?
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Study Notes
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
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Test your understanding of standard regression, error, and unique variance in statistics and data analysis.