# Regression On Standardized Variable

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## Regression On Standardized Variable

 Suppose Y and X are standardized and regression is run on the standardized variables. What will be the relation b/w residuals ie the original error term ui and the error term ui* of new model? I m getting ui* = (ui)/SD of Y.                                      (Where ui, ui* are all estimators nd SD stands for Standard deviation) Someone please confirm... Thanks
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## Re: Regression On Standardized Variable

 me too :)
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## Re: Regression On Standardized Variable

 OK thanks kangkan...one more question If There are two regression models i) LnY = ß1 + ß2*LnX + ui.         ( Ln stands for natural log) ii) LnY = a1 + a2*LnwX + ui*    (w is some positive constant) What will be the relation b/w intercept and slope coefficients? I m getting ß2=a2 and a1 = ß1 - ß2*Lnw or a1= ß1 - a2*Lnw Please cpnfirm
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## Re: Regression On Standardized Variable

 I am getting something different..let me check may b i am committing a mistake somewhere..!!!  "I don't ride side-saddle. I'm as straight as a submarine"
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## Re: Regression On Standardized Variable

 In reply to this post by Dreyfus Its ok..I got the same answers a2=b2=(dy/dx)*(x/y) and a1=b1-a2*logW.  "I don't ride side-saddle. I'm as straight as a submarine"
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## Re: Regression On Standardized Variable

 In reply to this post by Dreyfus Hey...whch chapter d problems are concerned to???? Is it something stat related ??? As d regression term is dre...plzzz reply..I cud nt get d connection..
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## Re: Regression On Standardized Variable

 In reply to this post by Dreyfus CONTENTS DELETED The author has deleted this message.
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## Re: Regression On Standardized Variable

 In reply to this post by ani CONTENTS DELETED The author has deleted this message.
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## Re: Regression On Standardized Variable

 In reply to this post by Dreyfus pls explain the first one..hw did u find erroor term?thnx MA Economics DSE 2014-16
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## Re: Regression On Standardized Variable

 Sonia ...see the attached files of my workings,....IMG_20140616_212315.jpg IMG_20140616_212357.jpg
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## Re: Regression On Standardized Variable

 Thnxx MA Economics DSE 2014-16
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## Re: Regression On Standardized Variable

 @vaibhav.. If There are two regression models i) LnY = ß1 + ß2*LnX + ui.         ( Ln stands for natural log) ii) LnY = a1 + a2*LnwX + ui*    (w is some positive constant) What will be the relation b/w intercept and slope coefficients? I m getting ß2=a2 and a1 = ß1 - ß2*Lnw or a1= ß1 - a2*Lnw hw did you derive this...pls help
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## Re: Regression On Standardized Variable

 @shefali...I hv attached my workings....IMG_20140617_002553.jpg
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## Re: Regression On Standardized Variable

 In reply to this post by Shefali let log Y=Y' and log X=X' Now equation (1) can be written as, Y'=ß1 + ß2*X'+ ui. where ß2=Cov(X',Y')/Var(X'), ß1=mean(Y')-ß2*mean(X') Now consider equation (2), it can be written as, log Y=a1 + a2*(logX+logw)+ui* or, Y'=a1 + a2*(X'+logw)+ui* (since logY=Y' and logX=X') here a2=Cov(X'+log w,Y')/Var(X'+ log w) Now Cov(X'+log w,Y)=Cov(X',Y') And var(x'+log w)=var(x') (since variance is independent of change in origin). thus a2=Cov(X',Y')/Var(X')=ß2. Mean (X')=Mean(X')+log w. therefore a1=mean(Y')-a2*{Mean(X')+log w}, a1=mean(Y')-a2*Mean(x')-a2*log w. a1=mean(Y')-ß2*Mean(x')-ß2*log w. (since a2=ß2). thus a1=ß1-ß2*log w, (since ß1=mean(Y')-ß2*mean(X')).  "I don't ride side-saddle. I'm as straight as a submarine"
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## Re: Regression On Standardized Variable

 This post was updated on . In reply to this post by Dreyfus Guys one more ques If There are two regression models i) expY = ß1 + ß2*expX + ui.         ( exp stands for natural exponent) ii) expY' = a1 + a2*expX' + ui'    (Y'= Y+w1 nd X'= X+w2) What will be the relation b/w intercept, slope coefficient and residual term? I m getting these: a2 = ß2*e^(w1-w2)                                  a1 = ß1*e^w1                                   ui' = ui*e^w1 Please confirm.....
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## Re: Regression On Standardized Variable

 @vaibhav. In that pic after the eqn 3 b line how did you get next eqn and aftr that how is B2* and B2 equal?