W3: Multiple Regression || with A+ Guaranteed Solutions.
Multiple Regression correct answers An extension of correlation and bivariate regression.
Enables us to predict scores on a DV from a SET of IVs (ie, more than one predictor, IV).
What a multiple regression produces correct answers It produces an equation that best predicts
the Y or dependent variable (criterion variable) from several independent variables (predictor
variables).
Uses of a Regression Analysis correct answers It is used to evaluate how a DV is related to
several other IVs. You can tease out the contribution of each individual IV to the overall
relationship.
You can also use the procedure to control for the effects of certain IVs to determine the
subsequent contribution to the equation from other variables of interest.
Designed primarily for continuous data, but can handle discrete data if converted into
dichotomous variables -> dummy variable coding.
Data designed for MRs correct answers It is designed for continuous or interval measures so that
the max amount of info is used in the analysis, yet it can also accommodate nominal predictor
measures (dichotomous variables can be entered as is, while categorical variables with 3+
categories must be recoded by means of a special technique known as dummy variable coding).
Two problems with the bivariate approach correct answers (1) This approach fails to take into
consideration that the possibility that IV1 and IV2 are related. Eg: depression accounts for 64%
variance in alcohol, coping skills 49% - together accounting for an impossible 113%.
(2) If two different IVs are used to predict a DV and come up with different results, which
answer is correct? This approach doesn't allow us to distinguish this. Eg. Depression predicts
alcohol 9, coping 7.
Advantages of Multiple Regression correct answers • More realistic modelling of relationships
between variables - it corrects for correlations between IVs
• Produces ONE equation that best predicts the DV from a set of IVs
• Allows us to determine the combined influence of IVs on prediction of DV (how much do they
do together?)
• ...the relative contributions of IVs for prediction of DV (which IV predicts best/worst?)
• ... the level of improvement in prediction if we add another IV (or several) - what changes with
what IV(s)?
, Four Types of Research Questions answered by Multiple Regressions correct answers •
Combined predictive utility
• Importance of IVs
• Uniqueness
• Improvement in Prediction
Four Research Questions answered by Multiple Regressions correct answers 1) How much
variance do the IVs account for (in combination) in the DV? [Consult R^2 value]
2) What is the relative importance of each of the IVs in the model? [Compare beta weights]
3) Which IV contributes the most unique variance to prediction of the DV? [Check sr^2 ]
4) How much improvement in the model occurs when we add an additional IV (or group of
IVs)? [Check R^2 change]
Example Research Questions for Combined Predictive Utility correct answers For example:
• How much of the variability in alcohol use can we explain by knowing scores on all three of
these predictor variables? (R^2)
• Does knowing scores on the set of variables tell us anything meaningful about alcohol use? (ie,
better than chance prediction?) (Sig. ANOVA?)
Example Research Questions for Importance of IVs correct answers For example:
• Which variable is the best predictor of alcohol use? (Beta weights)
• Is knowledge of anxiety helpful in predicting alcohol use or can we do just as well with the
knowledge of only impulsivity and coping skills? (Significance of predictor)
Example Research Questions for Uniqueness correct answers For example:
• How much unique variance (non-overlapping contribution) in alcohol use does each IV
explain? (sr^2)
Example Research Questions for Improvement in Prediction correct answers For example:
• Can we improve the prediction of a DV by adding one or more IVs to the equation? (R^2
change)
• After controlling for age, gender, and family history, does knowing scores on impulsivity and
anxiety significantly improve prediction of alcohol use? (R^2 change at each step)
Multivariate Regression Equation (simple) correct answers DV = b1(IV1) + b2(IV2) + Constant
Multiple Regression correct answers An extension of correlation and bivariate regression.
Enables us to predict scores on a DV from a SET of IVs (ie, more than one predictor, IV).
What a multiple regression produces correct answers It produces an equation that best predicts
the Y or dependent variable (criterion variable) from several independent variables (predictor
variables).
Uses of a Regression Analysis correct answers It is used to evaluate how a DV is related to
several other IVs. You can tease out the contribution of each individual IV to the overall
relationship.
You can also use the procedure to control for the effects of certain IVs to determine the
subsequent contribution to the equation from other variables of interest.
Designed primarily for continuous data, but can handle discrete data if converted into
dichotomous variables -> dummy variable coding.
Data designed for MRs correct answers It is designed for continuous or interval measures so that
the max amount of info is used in the analysis, yet it can also accommodate nominal predictor
measures (dichotomous variables can be entered as is, while categorical variables with 3+
categories must be recoded by means of a special technique known as dummy variable coding).
Two problems with the bivariate approach correct answers (1) This approach fails to take into
consideration that the possibility that IV1 and IV2 are related. Eg: depression accounts for 64%
variance in alcohol, coping skills 49% - together accounting for an impossible 113%.
(2) If two different IVs are used to predict a DV and come up with different results, which
answer is correct? This approach doesn't allow us to distinguish this. Eg. Depression predicts
alcohol 9, coping 7.
Advantages of Multiple Regression correct answers • More realistic modelling of relationships
between variables - it corrects for correlations between IVs
• Produces ONE equation that best predicts the DV from a set of IVs
• Allows us to determine the combined influence of IVs on prediction of DV (how much do they
do together?)
• ...the relative contributions of IVs for prediction of DV (which IV predicts best/worst?)
• ... the level of improvement in prediction if we add another IV (or several) - what changes with
what IV(s)?
, Four Types of Research Questions answered by Multiple Regressions correct answers •
Combined predictive utility
• Importance of IVs
• Uniqueness
• Improvement in Prediction
Four Research Questions answered by Multiple Regressions correct answers 1) How much
variance do the IVs account for (in combination) in the DV? [Consult R^2 value]
2) What is the relative importance of each of the IVs in the model? [Compare beta weights]
3) Which IV contributes the most unique variance to prediction of the DV? [Check sr^2 ]
4) How much improvement in the model occurs when we add an additional IV (or group of
IVs)? [Check R^2 change]
Example Research Questions for Combined Predictive Utility correct answers For example:
• How much of the variability in alcohol use can we explain by knowing scores on all three of
these predictor variables? (R^2)
• Does knowing scores on the set of variables tell us anything meaningful about alcohol use? (ie,
better than chance prediction?) (Sig. ANOVA?)
Example Research Questions for Importance of IVs correct answers For example:
• Which variable is the best predictor of alcohol use? (Beta weights)
• Is knowledge of anxiety helpful in predicting alcohol use or can we do just as well with the
knowledge of only impulsivity and coping skills? (Significance of predictor)
Example Research Questions for Uniqueness correct answers For example:
• How much unique variance (non-overlapping contribution) in alcohol use does each IV
explain? (sr^2)
Example Research Questions for Improvement in Prediction correct answers For example:
• Can we improve the prediction of a DV by adding one or more IVs to the equation? (R^2
change)
• After controlling for age, gender, and family history, does knowing scores on impulsivity and
anxiety significantly improve prediction of alcohol use? (R^2 change at each step)
Multivariate Regression Equation (simple) correct answers DV = b1(IV1) + b2(IV2) + Constant
