- #1

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- Homework Statement
- You have a linear model y = a+bx. Using the mean square error function for a zeroth order model (b=0 and a = <y>) and a first order model b=Covariance(x,y)/Variance(x) and a = <y> - b<x> show that E1/E0 = 1-r^2

- Relevant Equations
- MSE function E = <(y - a -bx)^2>

Correlation coefficient r = Covariance(x,y)/Standardev(x)Standarddev(y)

Standarddev = Square root of variance

The zeroth order model gives E0 = Var(y)

I've tried two methods:

Calculating 1-r^2 and trying to get E1/E0.

Calculating E1/E0 and trying to get 1-r^2.

I've tried two methods:

Calculating 1-r^2 and trying to get E1/E0.

Calculating E1/E0 and trying to get 1-r^2.