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# Linear Regression
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# Linear Regression
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This document contains information regarding the Odinary Least Squares linear regression implemented in the evaluation tool of the visualtisation platform.
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This document contains information regarding the Ordinary Least Squares linear regression implemented in the evaluation tool of the visualisation platform.
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## Model
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## Model
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... | @@ -36,7 +36,7 @@ with _E_(ε) = 0, it becomes : |
... | @@ -36,7 +36,7 @@ with _E_(ε) = 0, it becomes : |
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and we assumed normality so Var(ε) = _E_(εε') = σ<sup>2</sup>_I_, where σ<sup>2</sup> > 0 is the common variance/error of each element in the vector of errors or the mean-squared error. This gives us:
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and we assumed normality so Var(ε) = _E_(εε') = σ<sup>2</sup>_I_, where σ<sup>2</sup> > 0 is the common variance/error of each element in the vector of errors or the mean-squared error. This gives us:
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* Var(β<sup>_e_</sup>) = (__X'X__)<sup>-1</sup>__X'__ σ<sup>2</sup>_I_ __X__(__X'X__)<sup>-1</sup>
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* Var(β<sup>_e_</sup>) = (__X'X__)<sup>-1</sup>__X'__ σ<sup>2</sup>_I_ __X__(__X'X__)<sup>-1</sup>
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simplifing this, we get the error or variance for each coefficient given by
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simplifying this, we get the error or variance for each coefficient given by
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* Var(β<sup>_e_</sup>) = σ<sup>2</sup>(__X'X__)<sup>-1</sup>
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* Var(β<sup>_e_</sup>) = σ<sup>2</sup>(__X'X__)<sup>-1</sup>
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... | | ... | |