Regression Analysis
General Terms Overview
➔ predictor variable: the independent variable
➔ criterion variable: outcome measure (the DV)
➔ moderators: a factor that can affect the directionand/or strength of relationship of the
independent and dependent variables being measured
➔ mediators: causal impact
➔ selection threat: the possibility of participants/comparisongroups differing prior to the
treatment in regards to factors that aren’t being measured
➔ bivariate correlational designs: correlation studiesthat examine linear association between
twomeasured variables
◆ the limitations of this design
● type 1 error: running multiple analyses within thesame sample of participants
increase risk of type 1 error
● non-hierarchical: doesn’t allow for examining multiplecomplex patterns of
association; correlational analyses only examine the association between one
predictor and one outcome variable
Regression Analyses
➔ prediction line: the correlation between the variablescan be visualized as a line of best fit
through the data points
➔ can be used to describe existing dataandto makepredictions about new cases
➔ the main goal is to rule out alternative explanations
➔ multiple regression analysis
◆ analytical approach that allows for examining the association between multiple
predictor variables in a single criterion
◆ key advantage: allows for examining associations simultaneouslyand hierarchically
which controls for type 1 error due to there only being one analysis rather than many
➔ two common regression methods
◆ simultaneous regression: used to examine which ofthe multiple predictor variables is
the most strongly predictive of the outcome variable
● controls fortype 1 error
◆ hierarchical regression: examine if a variable/setof variables predicts the outcome
beyond a set of controlled variables
● controls fornon-hierarchical
➔ beta coefficients: communicate the strength and directionof the slope of the fitted line
(y=mx +b)
◆ unstandardized beta coefficient (b): describes theslope in the original unit of
measurement
● helpful when using regression analyses to make predictions about new cases
, ● >1 / -1 and have a standard error associated with it [in charts you will see b(SE)]
◆ standardized beta coefficients (𝛽): converts theslope into a standardized correlation
coefficient that varies between -1 and +1 and is interpreted similarly to coefficientr
● same effect size conventions as correlationr
◆ standard error of the estimate: the average amountof error that exists between the data
points and the line
● associated with unstandardized 𝛽
● when the prediction line “fits” the data well, there’s less standard error and
more accurate predictions
● when the prediction line doesn’t “fit” the data well, there is more standard error
and less accurate predictions
Factors That Bias Prediction
➔ curvilinear patterns: fitting prediction lines whenthe data is nonlinear can be bias
predictions
◆ standard correlations and simple analyses don’t work when the data is curvilinear
➔ outliers: extreme cases canpullthe prediction lineand bias the accuracy of predictions
➔ restriction of range: sampling too narrow of a rangeof data can bias predictions
➔ extrapolating beyond the data: inferring beyond therange of data biases predictions
◆ ‘predict’ future data flow [i.e. arrow pointing up for the iphone and sleep study even
though that wasn’t seen in the actual data]
◆ overgeneralization basically
Multivariate Designs
➔ multivariate designs: designs that include multiplepredictors of an outcome variable
➔ the kinds of variables found in this design
◆ controls: potential confounds that are identified,measured, and controlled for
◆ predictors: the key independent variables, treatments,or predictor variables of interest
◆ explainers: includes moderators (when an effect occurs)and mediators (why an effect
occurs)
◆ criterion: the key outcome variables of interest
➔ moderators vs mediators
◆ moderatorsindicate when (or in what context) an effectis most or least likely to occur
● interactions between variables indicated when a moderator is present
◆ mediatorsexplain the relationship between two variables
● why an effect occurs
Interpreting Regression Coefficients
➔ beta coefficients: strength and direction of an effect
General Terms Overview
➔ predictor variable: the independent variable
➔ criterion variable: outcome measure (the DV)
➔ moderators: a factor that can affect the directionand/or strength of relationship of the
independent and dependent variables being measured
➔ mediators: causal impact
➔ selection threat: the possibility of participants/comparisongroups differing prior to the
treatment in regards to factors that aren’t being measured
➔ bivariate correlational designs: correlation studiesthat examine linear association between
twomeasured variables
◆ the limitations of this design
● type 1 error: running multiple analyses within thesame sample of participants
increase risk of type 1 error
● non-hierarchical: doesn’t allow for examining multiplecomplex patterns of
association; correlational analyses only examine the association between one
predictor and one outcome variable
Regression Analyses
➔ prediction line: the correlation between the variablescan be visualized as a line of best fit
through the data points
➔ can be used to describe existing dataandto makepredictions about new cases
➔ the main goal is to rule out alternative explanations
➔ multiple regression analysis
◆ analytical approach that allows for examining the association between multiple
predictor variables in a single criterion
◆ key advantage: allows for examining associations simultaneouslyand hierarchically
which controls for type 1 error due to there only being one analysis rather than many
➔ two common regression methods
◆ simultaneous regression: used to examine which ofthe multiple predictor variables is
the most strongly predictive of the outcome variable
● controls fortype 1 error
◆ hierarchical regression: examine if a variable/setof variables predicts the outcome
beyond a set of controlled variables
● controls fornon-hierarchical
➔ beta coefficients: communicate the strength and directionof the slope of the fitted line
(y=mx +b)
◆ unstandardized beta coefficient (b): describes theslope in the original unit of
measurement
● helpful when using regression analyses to make predictions about new cases
, ● >1 / -1 and have a standard error associated with it [in charts you will see b(SE)]
◆ standardized beta coefficients (𝛽): converts theslope into a standardized correlation
coefficient that varies between -1 and +1 and is interpreted similarly to coefficientr
● same effect size conventions as correlationr
◆ standard error of the estimate: the average amountof error that exists between the data
points and the line
● associated with unstandardized 𝛽
● when the prediction line “fits” the data well, there’s less standard error and
more accurate predictions
● when the prediction line doesn’t “fit” the data well, there is more standard error
and less accurate predictions
Factors That Bias Prediction
➔ curvilinear patterns: fitting prediction lines whenthe data is nonlinear can be bias
predictions
◆ standard correlations and simple analyses don’t work when the data is curvilinear
➔ outliers: extreme cases canpullthe prediction lineand bias the accuracy of predictions
➔ restriction of range: sampling too narrow of a rangeof data can bias predictions
➔ extrapolating beyond the data: inferring beyond therange of data biases predictions
◆ ‘predict’ future data flow [i.e. arrow pointing up for the iphone and sleep study even
though that wasn’t seen in the actual data]
◆ overgeneralization basically
Multivariate Designs
➔ multivariate designs: designs that include multiplepredictors of an outcome variable
➔ the kinds of variables found in this design
◆ controls: potential confounds that are identified,measured, and controlled for
◆ predictors: the key independent variables, treatments,or predictor variables of interest
◆ explainers: includes moderators (when an effect occurs)and mediators (why an effect
occurs)
◆ criterion: the key outcome variables of interest
➔ moderators vs mediators
◆ moderatorsindicate when (or in what context) an effectis most or least likely to occur
● interactions between variables indicated when a moderator is present
◆ mediatorsexplain the relationship between two variables
● why an effect occurs
Interpreting Regression Coefficients
➔ beta coefficients: strength and direction of an effect
