In the squid data, all measurements are related to overall size of the beak. It may be useful to retain one measurement of size, say, W, and express the rest as ratios to W. The resulting ratios may then measure shape characteristics and exhibit less multicollinearity. Since the variables used in the regression are logarithms, the logarithms of the ratios are differences. For example, log(RL/W)=log(RL)−log(W).Using these redefinitions and keeping log(W) as is, we obtain the results shown in Table 8.14..

 

Table 8.14 Regression with Redefined Variables Model: MODEL 1 Dependent Variable: WT Source Model Error C Total Root MSE Dep Mean C.V. Variable RL WL RNL NWL W INTERCEP 1 1 INTERCEP RL WL DF 5 16 21 RNL NWL W DF 1 Variable DE 1 1 1 Analysis of Variancel Sum of Squares 17.92766 0.32116 18.24883 0.14168 R-square 1.07156 Adj R-q 13.22173 Parameter Estimate Variance Inflation Mean Square 1 0.00000000 1 3.58553 0.02007 2.401917 1.192555 -0.769314 0.79031542 1.035553 0.66679027 0.58251746 1.073729 3.376507 0.17920582 8.53690485 1 7.15487734 1 4.35395220 1 4.94314166 1 3.61063657 Dependent Variable: WT Test: ALLOTHER Parameter Estimates. Standard Error Numerator: Denominator: 0.72761686 0.81846940 F Value 0.1441 0.020073 178.627 0.9824 0.9769 3.301 1.457 T for H0: Parameter = 0 -0.973 1.553 1.843 18.842 de: df: 4 Prob > F 16 0.0001 Prob T 0.0045 0.1644 0.3448 0.1400 0.0839 0.0001 F val Prob > F: 7.1790 0.0016