Table 15.3 contains a portion of the data reported by Thompson and Randall-Maciver (1905) dealing with skull measurements of male Egyptians from different time periods. Here, only the data from 4000 BC and 150 AD are reported. Pool the data from both periods and create a smooth using rplot, kerreg, and lplot. What do these smooths suggest about the association between X and Y ? Check this possibility with the R function lintest in Section 15.8.1.

Note: The author’s web page contains the file skull.dat. There are four skull measurements in columns 1 through 4, with the time period stored in column 5. The two measures used here are in columns 2 and 3. If these data are stored in the R variable skull, here is one way of separating the data into R variables that can be used to do the analysis:

z=fac2list(skull[,2],skull[,5])

x4000=z[[1]]

x150=z[[5]]

zz=fac2list(skull[,3],skull[,5])

y4000=zz[[1]]

y150=zz[[5]]

The command x=c(x4000,x150) pools the X values and y=c(y4000,y150) pools the Y values.

TABLE 15.3: Skull Measurements X (4000 BC) 138 131 132 132 143 137 130 136 134 134 138 121 129 136 140 134 137 133 136 131 133 135 124 134 130 135 132 129 136 138 X (150 AD) 123 131 126 134 127 138 138 126 132 135 120 136 135 134 135 134 125 135 125 129 136 129 126 124 127 125 128 135 129 133 Y (4000 BC) 89 92 99 96 100 89 108 93 102 99 95 95 109 100 100 97 103 93 96 101 102 103 93 103 104 100 93 106 114 101 Y (150 AD) 91 95 91 92 86 101 97 92 99 92 95 101 95 93 96 95 99 96 92 89 92 97 88 91 97 85 81 103 87 97 Note: X is Basibregmatic Height of Skull; Y is Basialveolar Length of Skull