That's where the lack of fit F-test comes into play. Let's return to the first checking account example, (rouwverzen.net): Jumping ahead to the punchline, here's Minitab's output for the lack of fit F-test for this data set: As you can see, the lack of fit output appears as a portion of the analysis of variance table. rouwverzen.net(resids) #get Lilliefors (Kolmogorov-Smirnov) test for normality (nortest package must be installed) rouwverzen.net(resids) #get Pearson chi-square test for normaility (nortest package must be installed) rouwverzen.net(resids) #get Shapiro-Francia test for normaility (nortest package must be installed) Lack-of-fit test. ¾ Model 2 is telling R to consider Height as a “Factor” instead of a continuous variable, thus treating it as categorical and fitting the mean at each height. SSE(F) = = SSE(PE) [F = Full, PE = pure error] ¾ The Lack of Fit SSE is SSE(LF) = SSE(R) – SSE(F) = – = .

Lack of fit test in r code

Using R for lack-of-fit F-test. where df_1 is the degrees of freedom for SSLF (lack-of-fit sum of squares) and df_2 is the degrees of freedom for SSPE (sum of squares due to pure error). In R, the F-test (say for a model with 2 predictors) can be calculated with anova(lm(y~x1+x2), lm(y~factor(x1)*factor(x2))). #R code: Discussion 4. Sta, Fall , Utts #Lack-of-fit test #Ho: usual linear model holds #Ha: population average GPA at ACT level j is mu_j. rouwverzen.net(resids) #get Lilliefors (Kolmogorov-Smirnov) test for normality (nortest package must be installed) rouwverzen.net(resids) #get Pearson chi-square test for normaility (nortest package must be installed) rouwverzen.net(resids) #get Shapiro-Francia test for normaility (nortest package must be installed) Lack-of-fit test.

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