I occasionally have a need to perform multiple linear regression analysis calculations on accelerated testing of plastic piping. The fitted regression equations are used to extrapolate time to failure results to end use temperature and internal pressure conditions that are well outside of those employed in the accelerated testing. In doing this, it is desirable to perform a lack of fit test on the resultant regression equation to assess whether extrapolation of this type is justified. For the lack of fit test the residual sum of squares SS(E) has to be broken down into a “lack of fit” sum of squares and a “pure error” sum of squares. These two, when summed, equal the residual sum of squares. The pure error sum of squares is derived from data obtained on replicate tests under the same conditions (i.e. with the same independent variables employed). The Lack of Fit SS is obtained by subtraction. The mean squares are then calculated form the sums of squares and the appropriate degrees of freedom for each. The F ratio for the test is then = Lack of Fit Mean Square divided by the Pure Error Mean Square. The Null Hypothesis for this test is that the fit to the data is adequate. If the calculated F ratio is less than the critical value of F obtained from a table of such, the Null Hypothesis is accepted and one concludes that the regression equation with the fitted parameters adequately represents the data beyond the test conditions. If the F ratio exceeds the critical value from the table, the Null Hypothesis is rejected and one is supposed to go back to square one and try a different regression equation with the data in hand, at least for the purpose of extrapolating to conditions outside the boundaries of those employed in the accelerated test of interest My problem so far has been that the regression analysis package we have used only provides regression sum of squares and SSE results, it doesn’t break down SSE into its’ pure error and lack of fit components. Therefore, I have had to do that in a separate Excel spreadsheet in order to perform this particular analysis. My question here is are there statistics packages somewhere which will do that for me in order to speed up the process when I get into this type of calculation.
... View more