PSU STAT 501  Regression Plot (27 pages)
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 Pages:
 27
 School:
 Pennsylvania State University
 Course:
 Stat 501  Regression Methods
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Lack of Fit LOF Test An F test for checking whether a specific type of regression function adequately fits the data Example 1 Regression Plot Mortality 389 189 5 97764 Latitude S 19 1150 R Sq 68 0 R Sq adj 67 3 Mortality 200 150 100 30 40 50 Latitude Do the data suggest that a linear function is not adequate in describing the relationship between skin cancer mortality and Example 2 Regression Plot Weight 393 264 5 90235 Length S 54 0115 R Sq 83 6 R Sq adj 82 9 700 600 Weight 500 400 300 200 100 0 60 70 80 90 100 110 120 130 140 150 Length Do the data suggest that a linear function is not adequate in describing the relationship between the length and weight of an alligator Example 3 Regression Plot wgtloss 129 787 24 0199 iron S 3 05778 R Sq 97 0 R Sq adj 96 7 130 wgtloss 120 110 100 90 80 0 1 2 iron Do the data suggest that a linear function is not adequate in describing the relationship between iron content and weight loss due to corrosion Lack of fit test for a linear function Use general linear test approach Full model is most general model with no restrictions on the means j at each Xj level Reduced model assumes that the j are a linear function of the Xj i e j 0 1Xj The full model Yij j ij College entrance test score 30 5 2 20 4 1 10 3 0 1 2 3 High school gpa 4 5 College entrance test score The reduced model 22 Y E Y 0 1 x 18 14 10 6 Yi 0 1 x i 1 2 3 High school gpa 4 5 Assumptions and requirements The errors i and hence the responses Yi are independent The errors i and hence the responses Yi are normally distributed The errors i and hence the responses Yi have equal variances 2 for all x values The LOF test requires repeat observations called replicates for at least one of the X values Notation iron 0 01 0 01 0 01 0 48 0 48 0 71 0 71 0 95 1 19 1 44 1 44 1 96 1 96 wgtloss 127 6 130 1 128 0 124 0 122 0 110 8 113 1 103 9 101 5 92 3 91 4 83 7 86 2 c different levels of X c 7 with X1 0 01 X2 0 48 X7 1 96 nj number of replicates for jth level of X Xj n1 3 n2 2 n7 2
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