regression

[SoniaKapoor]

In the regression Yi = β1 + β2Xi + ui suppose if we add a constant value, say, 2, to each X value?
hw does it affect slope and intercept.?

[Akshay Jain]

no change in the slope coefficient as its value is independent of change of origin..but intercept will change ..(focus on the formulas of Beta1 and Beta2)

[Granpa Simpson]

The slope will remain the same..!!!

[SoniaKapoor]

Thanxxx!

[SoniaKapoor]

And what happens in following cases to intercept and coefficient
1. When X is divided by 2
2. when both X and Y are divided by 2

[Granpa Simpson]

when x is divided by 2, then Cov(X/2,Y)=1/2*Cov(X,Y)
Var(X/2)=1/4*Var(X).
Thus beta(slope estimate)=Cov(x/2,Y)/Var(X/2)=(1/2)*Cov(X,Y)/(1/4)*var(X)=2*{Cov(X.Y)/Var(x)}=2*beta of original regression function.
Similarly when both X and Y are divided by 2, then Cov(X/2,Y/2)=(1/4)*Cov(X,Y) and Var(X/2)=(1/4)*Var(X), Thus beta=Cov(X/2,Y/2)/Var(X/2)=Cov(X,Y)/Var(X)=original beta, hence it remains unchanged.
Similarly you can compute intercept terms too by using definitional formulas..!!!!!

[SoniaKapoor]

i'm getting in both cases intercept increases..!Please confirm Allen