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Covariance and variance doesn't make sense for realised (non-stochastic) variables. So removed the expressions with them and expanded the last term. |
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:<math>\hat{y_i} = \hat{a} + \hat{b}x_i</math>
:<math>\bar{y} = \hat{a} + \hat{b}\bar{x}</math>
:<math>\hat{b
So,
:<math>\hat{y_i} - \bar{y} = \hat{b}(x_i - \bar{x})</math>
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Therefore,
:<math>\sum_{i=1}^n 2(\hat{y}_i-\bar{y})(y_i-\hat{y}_i) = 2\hat{b}\sum_{i=1}^n (x_i-\bar{x})(y_i-\hat{y}_i) = 2\hat{b}\sum_{i=1}^n (x_i-\bar{x})((y_i - \bar{y}) - \hat{b}(x_i - \bar{x}))</math>
:<math>
==Partitioning in the general ordinary least squares model==
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