Lab 4: IML and REG Example: 1. Dowdy and Wearden (1983) presented a set of data containing 14 measurements on the following variables, with results as shown in the table that follows. C1 : the number of larvae of the Chaoborus (which resembles the mosquito in appearance but not in blood-sucking behavior) collected in a grab sample of the sediment from an area of approximately 225 cm 2 of lake bottom C2 : the depth(m) of the lake at sampling point C3 : the brackishness (conductivity, recorded in mhos per decimeter) of the water at the bottom C4 : the dissolved oxygen (mg/l) in the water at the bottom Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Number of Larvae 35 10 9 30 20 23 28 8 29 4 18 14 32 6 Depth of lake 8.4 2.0 3.5 10.4 6.5 6.2 12.4 7.0 5.8 3.0 6.0 5.5 9.0 1.1 Based on the output answer the following questions: 1. Give the regression equation in terms of the data. Brackishness of water 8 6.5 6.2 5.0 6.5 7.3 6.4 6.0 6.1 5.4 7.3 6.6 6.5 5.8 Dissolved Oxygen 1 8.5 6.5 1.5 7.5 4.5 4.0 10.0 3.0 11.0 4.5 5.5 2.5 7.0 THE PROC IML for the estimation: data abc; input Int y x1 x2 cards; 1 35 8.4 1 10 2.0 1 9 3.5 1 30 10.4 1 20 6.5 1 23 6.2 1 28 12.4 1 8 7.0 1 29 5.8 1 4 3.0 1 18 6.0 1 14 5.5 1 32 9.0 1 6 1.1 run; x3; 8 6.5 6.2 5.0 6.5 7.3 6.4 6.0 6.1 5.4 7.3 6.6 6.5 5.8 1 8.5 6.5 1.5 7.5 4.5 4.0 10.0 3.0 11.0 4.5 5.5 2.5 7.0 proc iml; /*invoking iml*/ use abc; read all var{Int x1 x2 x3} into x; read all var{y} into y; n=nrow(x); k=ncol(x); tx=t(x); /*taking transpose*/ xtx=t(x)*x; print xtx x tx; /*X'X*/ d1=det(xtx); /*finding inverse*/ s1=inv(xtx); est=s1*tx*y; print d1 s1 est; e=y-x*est; sse=t(e)*e; mse=sse/(n-k-1); print e sse mse; var=mse*s1; print est var; run; In REG this would be: PROC REG DATA=ABC; MODEL y=x1 x2 x3; RUN;