1 / 7

Regression Models with 2 quantitative variables (& Interaction)

Regression Models with 2 quantitative variables (& Interaction). 2 quantitative variables main effects model with no interaction interaction model. 2 centered quant vars y ’ = b 0 + b 1 x 1 + b 2 x 2 “ X 1 ” is a centered quantitative variable X 1  X 1 – X 1mean

wilona
Download Presentation

Regression Models with 2 quantitative variables (& Interaction)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Regression Models with 2 quantitative variables (& Interaction) 2 quantitative variables main effects model with no interaction interaction model

  2. 2 centered quant vars y’ = b0+ b1x1+ b2x2 “X1” is a centered quantitative variable X1 X1 – X1mean “X2” is a centered quantitative variable X1 X1 – X1mean

  3. 2 centered quant vars y’ = b0+ b1x1+ b2x2 b0 mean of those in Cz with X=0 (mean) b1 slope of Y-X1 regression - slope same for all values of X2 no interaction b2 slope of Y-X2 regression - slope same for all values of X1 no interaction

  4. 3a Xs are centered quant variables (both are standardized std = 1) y’ = b0 + b1X1 + b2X2 b0 = ht of X2mean line b1 = slope of X2mean line +1std X2 b2 = htdifs among X2-lines 0 10 20 30 40 50 60 X2=0 X2-lines all have same slp (no interaction) -1std X2 -2 -1 0 1 2  X

  5. 2 centered quant var & their product term/interaction y’ = b0+ b1x1+ b2x2+ b3xz “X1” is a centered quantitative variable X1 X1 – X1mean “X2” is a centered quantitative variable X1 X1 – X1mean “XZ” represents the interaction of “X1” and”X2”

  6. 2 centered quant vars & their interaction y’ = b0+ b1x1+ b2x2+ b3xz b0 mean of those in Cz with X=0 (mean) b1 slope of Y-X1 regression - Simple Y-X1 slope for X2 mean=0 b2 slope of Y-X2 regression - Simple Y-X2 slope for X1 mean=0 b3  interaction of X1 & X2 - how slope of Y-X1 reg lines change with X2 value - how slope of Y-X2 reg lines change with X1 value

  7. 3b 2 quantitative predictors w/ interaction (both are standardized std = 1) Xcen = X – Xmean Zcen = Z – Xmean ZX = Xcen * Zcen y’ = b0 + b1Xcen + b2Zcen + b3XZ a = ht of Zmean line b3 b1 = slope of Zmean line b1 b2 = htdifs among Z-lines b2 +1std Z b3 0 10 20 30 40 50 60 b3 = slpdifs among Z-lines -b2 Z=0 -1std Z b0 -2 -1 0 1 2  Xcen

More Related