By Simon Sheather
This ebook specializes in instruments and strategies for development legitimate regression types utilizing real-world information. A key subject matter during the booklet is that it simply is smart to base inferences or conclusions on legitimate types.
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Additional info for A Modern Approach to Regression with R (Springer Texts in Statistics)
If the regression of Y on X is linear, then for i = 1, 2, …, n Yi = E(Y | X = x ) + ei = b 0 + b1 x + ei where ei is the random error in Yi and is such that E(e | X) = 0. The random error term is there since there will almost certainly be some variation in Y due strictly to random phenomenon that cannot be predicted or explained. In other words, all unexplained variation is called random error. Thus, the random error term does not depend on x, nor does it contain any information about Y (otherwise it would be a systematic error).
4. 5. 6. 7. 1 The plots enable us to assess visually whether the assumptions are being violated and point to what should be done to overcome these violations. Determine which (if any) of the data points have x-values that have an unusually large effect on the estimated regression model (such points are called leverage points). Determine which (if any) of the data points are outliers, that is, points which do not follow the pattern set by the bulk of the data, when one takes into account the given model.
3 A plot of the production data with the least squares line of best fit Since b0 and b1 are unknown all we can do is estimate these errors by replacing b0 and b1 by their respective least squares estimates bˆ0 and bˆ1 giving the residuals eˆi = Yi − (bˆ 0 + bˆ 1 xi ) = Yi − estimated regression line at xi . These residuals can be used to estimate s 2. In fact it can be shown that S2 = RSS 1 n 2 = ∑ eˆi n − 2 n − 2 i =1 is an unbiased estimate of s 2. Two points to note are: 1. eˆ = 0 (since ∑ eˆi = 0 as the least squares estimates minimize RSS = ∑ eˆi2 ) 2.
A Modern Approach to Regression with R (Springer Texts in Statistics) by Simon Sheather