It is intuitively clear that if the iterative process is slowly convergent, then (6.8) can be satisfied even if the exact error || x n − x|| is much larger than ACCUR.ĭifficulties that may arise when (6.9 ) is used. (B) Difficulties related to the traditional stopping criteriaĭifficulties which may arise when (6.8 ) is used. In fact, the original data was generated from the model This is a better model than that derived in Example 7.1 because the absolute values of the t-ratios are now all greater than 2. The data array is not shown in the script e4s706.m. Using the same data as Example 7.1, fit a regression model using the explanatory variables x 1 and x 2 only. Either we have a recording error in this particular observation or the data is correct and thus the model we are using fits this particular data point poorly. If we change the last value of y to −8.3 (and showing the analysis of the residuals only), we haveįor the observation y = − 8.3, we see that the residual, the standard residual, and Cook's distance are all large, compared with the values for the rest of the data. This suggests that x 3 does not make a significant contribution to the model and can be removed. The coefficient of x 3 is small, and, more importantly, the corresponding absolute value of the t-ratio is very small (it is in fact not zero, but −0.0032).
(To save space the data is given in the form required by the function mregg2.) The first row, second, and third rows of the matrices are the values of the explanatory variables x 1, x 2, and x 3, respectively, and the fourth row contains the corresponding values of y. Residuals appear in many areas in mathematics, including iterative solvers such as the generalized minimal residual method, which seeks solutions to equations by systematically minimizing the residual.Fit a regression model to the data given by X0, X1, and Xd in script e4s705.m. When one does not know the exact solution, one may look for the approximation with small residual. In these cases, the initial equation is considered as well-posed and the residual can be considered as a measure of deviation of the approximation from the exact solution. Given an approximation x 0 of x, the residual isī − f ( x 0 ) To be precise, suppose we want to find x such that Loosely speaking, a residual is the error in a result.
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