L8 W5 Multiple Regression

Regression line (intercept, slope/ regression coefficient); Regression coefficient: B and beta; R^@, RMSE

how is multiple regression connected to regression and correlation?

• regression extends correlation

  • allows us to predict scores on one variable (Y) from scores on another variable (simple regression)

• multiple regression allow us to predict scores on Y variable from a number of X variables

what is the conceptual understanding of multiple regression?

what is the equation for multiple regression? what applications does it have?

• Regression line is a linear combination of the Xs

• Very common in research and applied settings

  • Øpredict success in a job from …

    • •grades, cognitive ability test, quality of letters of reference

  • Øpredict prosocial behavior from …

    • •empathic concern, perspective taking, gender

what does multiple regression allow us to do that is new?

1.Determine how much variance in the criterion is accounted for by a group of predictors (R²)

2.Determine the “unique” or “incremental” contribution of each predictor

what is meant by “unique” contribution of each X?

• multiple regression allows us to examine the relation between each predictor (X) and the criterion (Y), after statistically controlling the other predictors in the model

• •Important when our predictors (Xs) are correlated (very common)

• •We can exert “control” over our predictors

what are some research examples of multiple regression?

• Interested in predicting depression (Y) from:

  • •Negative life events (X₁)

  • •SES (X₂)

• Interested in predicting life satisfaction (Y) from:

  • •Age (X₁)

  • •Income (X₂)

what are the things to consider when looking at stastical control in multiple regression? CAN DELETE

zero order correlations

considering what multiple regressions is doing

looking at “control” in multiple regressions

semi-partial

what is there to consider with zero order correlations?

• zero order means the correlation btwn two variables with no other variables statistically controlled

  • people usually don’t say “zero order”- assume it is, unless otherwise stated

what is multiple regression doing?

what is “control” in multiple regression?

what is semi-partial r?

betas'/standardized regression coefficients are equivalent to semi-partial r

there are many possible results with statistical control in multiple regression. what might happen if X₁ and X₂ are both related to the criterion, but they are also highly related to each other?

how does the multiple regression equation change from simple regression?

• In multiple regression, the regression coefficients are called “partial regression coefficients,” so the interpretation of “a” and “b” changes from simple regression

• a (intercept): predicted Y when all predictors (X₁..._k) are zero

• b₁ (slope): expected change in Y per unit change in X_1, controlling for the other predictors. Partial unstandardized regression coefficient

• Beta_1: the relation of  X₁ and Y, controlling for the other predictors. Partial standardized regression coefficient. Equivalent to a “semi-partial correlation”

how do we run multiple regression in jamovi?

what does the output of jamovi tables mean?

from these unstandardized regression coefficients, what do these numbers tell us?

• Y' = 4.92 + .08(incivility) – .79(stress)

• •b for X₁:  For every unit increase in incivility, job satisfaction increases by .08 units, after controlling stress

• •b for X₂:  For every unit increase in stress, job satisfaction decreases .79 units, after controlling incivility

what is happening with incivility? (X1)

• •zero-order correlation: Incivility (X₁) & Job Sat (Y).

• r = -.67, p = <.001

• •but when we control for Stress (X₂), Beta = .08, p = .765

• Why? Because Beta is a semi-partial correlation

contrast simple regression with both the model fit table and the coefficients table

what is a conceptual summary of regression?

• •Allows us to predict scores on variable (Y) from scores on another variable (simple regression) or from a set of variables (multiple regression)

• •From multiple regression, we can ascertain the unique predictive power of a number of predictors

• Heads up: The latter relates to the concept of ‘Incremental Validity’ which we will discuss more in validity lectures

review the additional multiple regression run in jamovi, using the annotated output