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Lecture Notes 5
1. GoodnessofFit
The goodnessoffit measure is, R
2
.
SST
SSE
R
1
2
If R
2
= 0, then no fit
If R
2
= 1, then a perfect linear fit
Also, n = k which is algebraic system
Problem – As the number of x variables increases, R
2
always gets
larger
Adjusted R
2
Penalize the goodness of fit if more variables are added
penalty
error
R
k
n
n
R
R
1
1
)
1
(
1
2
2
2
.
As the number of independent variables increase, the penalty
increases, but the error could decrease if new variables explain ‘y’
better.
Sometimes
2
R
can be negative, indicating a very poor fit
Note – Very important; it has to be the same y variable
One model it cannot be y and in another it is ln (y)
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2. Maximum Likelihood
Assume the residuals and y variable has a known distribution, usually
the normal distribution.
An algorithm finds the parameters that maximizes this distribution
The total value of the distribution is L(…) or ln L(….)
Distributions are not linear, like the normal
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 Fall '11
 BLAIR

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