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2023-03-28 09:43:54 本頁(yè)面
【正文】 1 Observed Value Observed Value Y 6 Sample Linear Regression Model e i = random error Y X Y b b X e i i i ? ? ? 0 1 ^ Y b b X i i ? ? 0 1 Unsampled Observed Value Sampled Observed Value 7 Ordinary Least Squares The least squares method provides an estimated regression equation that minimizes the sum of squared deviations between the observed values of the dependent variable yi and the estimated values of the dependent variable . yi^e 2 Y X e 1 e 3 e 4 Y b b X e i i i ? ? ? 0 1 ^ Y b b X i i ? ? 0 1 OLS Min e e e e e i i 2 1 1 2 2 2 3 2 4 2 ? ? ? ? ? ? Predicted Value 8 Coefficient Equations Y b X b X Y n X Y X n X b Y b X i i i i i n i i n ? ? ? ? ? ? ? ? ? ? ? 0 1 1 1 2 2 1 0 1 Sample regression equation Slope for the estimated regression equation Intercept for the estimated regression equation b 9 Evaluating the Model ? Test Coefficient of Determination and Standard Deviation of Estimation ? Residual Analysis ? Test Coefficients of Significance ^ Y b b X i i ? ? 0 1 10 Measures of Variation in Regression 1. Total Sum of Squares (SST) Measure the variation between the observed value Yi and the mean Y. 2. Explained Variation (SSR) Variation caused by the relationship between X and Y. 3. Unexplained Variation (SSE) Variation caused by other factors. 11 Variation Measures Y X ? Y X i SST (Yi Y)2 SSE (Yi Yi
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