Monday, February 29, 2016 Lecture 2/29 ! Multiple Regression Analysis! Regression Review - Can test r, t, or F to see if regression equation is signicant ! F: look at \"F\" and \"Sig\" on computer output! r: look under \"B\" across from the variable for coefcient ! Error Review - The stronger the correlation, the better the prediction! - Standard error of the estimate (SEE): a measure of how much error is in our prediction (i.e. how accurate is our prediction?) ! \"r\" and \"SEE\" are inversely related! Testing for Statistical Significance Review - Does the regression equation (or \"model\") predict the criterion variable better than chance?! Can test r, t, or F to see if regression equation is signicant ! F ratio used in regression: F = variance predicted/variance not predicted= MS regression/MS residual! Other Issues with Regression - Dummy coding can be used when predictor (IV) is nominal, but criterion (DV) must always be interval/ratio! ex: male=1, female=0! Multiple Regression Analysis (MRA) ! Relationship of correlation and regression: 1 Monday, February 29, 2016 - Bivariate corr (rel. between X & Y) -> Bivariate reg (predicting Y from X)! - Multiple corr (rel. of Y with both X & Z) -> Multiple reg (predicting Y from both X & Z) ! Purpose of MRA - to predict one criterion variable (DV) from more than one predictor variables (IVs), and to see which combination of predictor variables makes the best prediction of the criterion variable ! The Multiple Regression Equation (or \"Model\") - the general goal of MRA is to select the fewest, best predictors of the criterion variable ! - so the best model is the one with the fewest predictive variables, and the variables have the most predictive power ! - Good: predictor variables not highly core with each other, but highly core with the criterion variable ! ! Y ! ! ! ! ! ! X2 X1 - Bad: predictor variables highly core with each other, and only slightly core with the criterion variable 2 Y X2 X1 Monday, February 29, 2016 - An extension of the bivariate regression equation:! Y=bX+a! - The multiple regression equation is:! ! - b: partial regression coefcients (\"partial slope\" shows unique relationship of each IV with the DV)! - a: constant (y-intercept) ! - EX: Predicting College GPA based on HS GPA, SAT scores, and partying! Y=college GPA, ! ! =HSGPA, b1=.31 =SAT, b2=.03 =partying! b3=-.72 ! a=2.5! college GPA= .31(HSGPA)+ .03(SAT) -.72(partying) +2.5! Assess the Overall Equation for Significance - Do the predictor variables (as a group) predict the criterion variable better than chance? ! ! Y ! ! Larger F ! ! X1 X2 ! ! ! Y ! ! X2 ! ! 3 X1 Smaller F Monday, February 29, 2016 - How well does the regression equation predict the criterion variable?! : the amount of variance in DV explained by the combination of predictor variables! ranges from 0-1! - 1= all the variance; 0= no variance 4 Monday, February 29, 2016 5