Psychology 3580F/G Lecture Notes - Lecture 4: Coefficient Of Determination, Concurrent Validity, Regression Analysis
22 May 2019
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Thursday, October 4th — Multiple Regression and Incremental Validity
•2 major aspects of validity
•validity of measurement
•content validity
•construct validity
•validity of decisions
•criterion-related validity —> correlation between predictor and criterion scores
•predictive validity
•concurrent validity
•main purpose of regression is to establish validity
•incremental validity refers to whether a new/additional variable enhances prediction beyond
what an existing predictor offers
•a bivariate correlation assesses the degree of a linear relationship between 2 variables (r)
•when you square a correlation you get the coefficient of determination (rsq) which is the
proportion of shared variance between the variables
•in a ven-diagram the unique variance would be where the circles don’t overlap while the
shared variance is located where the circles overlap
•regression is often used when the intent is prediction while correlations are often used when
intent is simply to assess relation between the DV and IV
•in bivariate correlation and bivariate regression b = r, but this will not be the same in multiple
regression since there’s more than one predictor variable
•bivariate regression allows us to make predication about people’s sores on a criterion variable
based on their actual performance on a predictor variable
•equation (representing a straight line) that describes changes in predicted criterion scores
(Y’) and a function of changes in score son the predictor (X)
•Y = a + b(X) where a = constant, b = beta weighted/regression coefficient (slope), and X is
the actual score
•Y = predicted criterion score
•regression coefficients (b) are the “weights” of variables
•regression analysis attempts to minimize squared errors of prediction
•predicted values of Y (Y’) are as close as possible to the actual values of Y such that (Y-
Y’)squared is as small as possible of the entire sample (i.e. least squares)
•multiple regression is an extension of bivariate regression in which there’s 1 DV and multiple
IVs
•denoted by R which is the correlation between the predicted and observed Y values
•always positive so it doesn’t show the direction of the relationship, only magnitude
•ranges from 0-1
•Y’ = a + b1(X1) + b2(X2) + … + bn(Xn)
•beta weights/regression coefficients serve to maximize the multiple correlation (R) and
minimize errors of prediction
•R is the shared relationship among your predictors with your outcome (X)
•R-squared is the squared multiple correlation which tells you the proportion of shared
variance between the criterion (DV) and the weighted set of predictors (IVs) in the
regression equation
•R-squared vs. adjusted R-squared
•validity shrinkage
•Rs obtained from a sample are generally inflated because they capitalize on sample-specific
characteristics
