1

In the Walpole et al. book on statistics, there are 2 graphs explaining the lack-of-fit component of SSE (error sum of squares - unexplained variation) in the simple linear regression model, 11.16 and 11.17. Also, there is a block of text describing them.

However, I can't visualize the SSR(regression sum of squares - amount od the y-variation explained by the model) component of total error in 11.16 and 11.17., having in mind that the SSR is the sum of (predicted values - sample mean)^2, and that the predicted values are based on these exact sample points we use to calculate SSE. descriptions11.16 and 11.17

Confused engineer
  • 13
  • 1
    Can you spell out more precisely what SSR and SSE mean. Those abbreviations can mean different things. – Sextus Empiricus Jan 16 '23 at 13:34
  • I am not sure what the problem is in this question. There seems to be some confusion, but I am not sure what. Examples of figures and computations of error=bias+variance might be helpful. – Sextus Empiricus Jan 16 '23 at 13:37
  • @SextusEmpiricus the textbook offered a visualization of the lack-of-fit component in regression model. I wonder if there's a simple way of visualizing the SSR in these examples - for instance one graph of a small SSR value and another one for a big SSR value. I think it would be easier to draw inferences from the visualizations, helping me and others to understand the relationships of these variables. – Confused engineer Jan 16 '23 at 14:59
  • You need the Y = Ybar horizontal line on the graph. Then SSR is just the sum of squared vertical deviations from the fitted line to that flat line. – BigBendRegion Jan 16 '23 at 15:38
  • I still didn't got the SSR and SSE so I started looking up a pdf on the internet to read that book, and I see that it is confusing. – Sextus Empiricus Jan 16 '23 at 16:21
  • You might be interested in the following question: Linear regression: F-test for lack of fit (using ANOVA to test regression model) - intuition? The image in my answer shows a linear fit and a fit at all points. This latter fit can be computed to obtain an unbiased estimate of the error. Lack of fit relates to the situation that the unbiased estimated of the error is smaller than the (biased) model fit (if there's lack of fit then the latter will be bigger). – Sextus Empiricus Jan 16 '23 at 16:23

0 Answers0