Dear Colleagues;
I derived the following equation using MINITAB:
pKi = - 10.9 + 3.77 Tu + 1.89 Tm + 5.55 Av
- 6.35 Ap + 37.0 Km - 71.6 Ks
Predictor Coef StDev T P VIF
Constant -10.894 2.798 -3.89 0.005
Tu 3.7654 0.6885 5.47 0.000 37.6
Tm 1.8904 0.4559 4.15 0.003 21.0
Av 5.550 1.100 5.05 0.000 2187.1
Ap -6.353 1.146 -5.54 0.000 2641.9
Km 37.034 8.609 4.30 0.003 34.7
Ks -71.61 14.21 -5.04 0.000 85.5
n = 15 SD = 0.5804 R-Sq = 89.6% F = 11.51
Since the variance inflation factors are so large I generated a
Pearson correlation maxtix:
Tu Tm Av Ap Km
Tm 0.261
Av 0.779 0.405
Ap 0.772 0.430 0.999
Km -0.173 0.525 -0.436 -0.415
Ks -0.036 0.368 -0.474 -0.463 0.931
As you see Ap and Av are colinear. So I thought to see what
would happen if either of these two variables were omitted from
the equation. When the data were regressed without Ap I
obtained
pKi = - 5.23 + 1.67 Tu + 0.284 Tm - 0.473 Av + 6.8 Km - 17.6 Ks
Predictor Coef StDev T P VIF
Constant -5.228 5.404 -0.97 0.359
Tu 1.672 1.194 1.40 0.195 26.3
Tm 0.2837 0.7302 0.39 0.707 12.5
Av -0.4735 0.3596 -1.32 0.220 54.3
Km 6.79 13.82 0.49 0.635 20.8
Ks -17.63 21.49 -0.82 0.433 45.4
n = 15 S = 1.204 R-Sq = 49.7% F = 1.78
whereas is Av is omitted I obtain
pKi = - 7.37 + 2.32 Tu + 0.694 Tm - 0.645 Ap + 11.3 Km - 29.9 Ks
Predictor Coef StDev T P VIF
Constant -7.366 5.223 -1.41 0.192
Tu 2.324 1.208 1.92 0.086 31.2
Tm 0.6935 0.7505 0.92 0.380 15.3
Ap -0.6447 0.3480 -1.85 0.097 65.6
Km 11.25 13.36 0.84 0.421 22.5
Ks -29.94 22.30 -1.34 0.212 56.6
n = 15 S = 1.119 R-Sq = 56.6% F = 2.34
My question is: why is there such a decline in the statistical
quality of the regression equation when one of the two colinear
variables (Av or Ap) is omitted?? Since Ap and Av are colinear,
I expected that removing one of them from the 6-variable
equation would have been compensated for by a change in the
coefficient preceding the other, accompanied by only a
negligible change in statistical quality of the 5-variable
equations compared to the 6-variable equation. Obvious this was
_not_ the case.
Responders should contact me _directly_ at
[EMAIL PROTECTED]
because I rarely log on to this usegroup.
Thanks in advance to all responders,
S. Shapiro
[EMAIL PROTECTED]
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