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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

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Regression Models with 2 quantitative variables (& Interaction)

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  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

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