Multiple Regression in Psychology: Concepts, Coefficients, and Model Evaluation

What is bivariate regression?

The prediction of a single outcome (Y) based on scores on a single predictor (X).

What is multiple regression?

The prediction of scores on a single criterion (Y) based on scores on multiple predictors (X1, X2, ...).

How does increasing the number of predictors affect the prediction of an outcome in multiple regression?

More predictors included lead to better prediction of the outcome, accounting for more variance.

What are the key components tested in multiple regression?

The overall relationship between Y and all predictors, and the magnitude of the relationship between Y and each individual predictor.

What is the purpose of the R-squared (R2) in multiple regression?

It measures the variance in Y jointly accounted for by all predictors.

What does adjusted R2 provide in multiple regression analysis?

A more conservative estimate of R2, accounting for the number of predictors in the model.

What does the unstandardized regression coefficient (b) represent?

The change in the outcome variable (Y) for a one-unit change in the predictor variable (X).

What is the significance of the standardized regression coefficient (β)?

It indicates the strength of the relationship between each predictor and the outcome variable, standardized for comparison.

What is a zero-order correlation (r)?

The unadjusted correlation coefficient between a given predictor (Xj) and Y, ignoring other predictors.

What is partial correlation (pr)?

The correlation between a given predictor (Xj) and Y after accounting for the variance explained by other predictors.

What is semi-partial correlation (sr)?

The correlation between a given predictor (Xj) and Y after accounting for the variance explained by other predictors, but only partialled out from Xj.

What is the regression equation for multiple regression with two predictors?

Ŷ = b1X1 + b2X2 + a, where Ŷ is the predicted outcome, b1 and b2 are regression coefficients, and a is a constant.

What is the significance of the F-test in multiple regression?

It tests the overall significance of the regression model.

What does a significant β indicate in multiple regression?

It means that the predictor adds unique information to the model.

What are the assumptions for trusting a multiple regression model?

Linear relationships, independent observations, well-behaved residuals, non-redundant predictors, and sufficient data.

What does it mean when predictors are correlated in a regression model?

It indicates that they may share variance in predicting the outcome, complicating the interpretation of their individual effects.

What is the impact of a missing important predictor in a regression model?

It can distort the roles of the included predictors and lead to misleading conclusions.

What does the term 'residual variance' refer to?

The leftover variance in Y that cannot be explained by the predictors in the model.

What does a higher R2 value indicate?

It indicates that a larger proportion of variance in the outcome variable is explained by the model.

What is the difference between prediction and causation in regression analysis?

Prediction shows which predictors track the outcome, while causation implies that changing predictors would change the outcome.

What is the regression equation for bivariate regression?

Ŷ = bX + a, where Ŷ is the predicted outcome, b is the regression coefficient, and a is a constant.

What does the term 'plane of best fit' refer to in multiple regression?

It describes the linear model that best represents the relationship between multiple predictors and the outcome variable.

What is the role of power analysis in regression modeling?

It helps determine the sample size needed to detect an effect if one exists.

What does 'well-behaved residuals' mean?

It means that the residuals are roughly normal and evenly spread across predicted scores.

What does it mean if a model fits beautifully but fails on new data?

It suggests that the model may be overfitting, capturing noise rather than the underlying relationship.