forecasting_lecture_05

forecasting_lecture_05 - Lecture Notes 5 1. Goodness-of-Fit...

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1 Lecture Notes 5 1. Goodness-of-Fit The goodness-of-fit 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 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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forecasting_lecture_05 - Lecture Notes 5 1. Goodness-of-Fit...

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