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I've a binary response (1 = event happen, 0 = otherwise) and 8 continuous predictors plus 1 categorical. Fitting in Minitab with a Binary Logistic Regression give me this output:

Binary Logistic Regression: Deformato versus A, B, C, D, E, F, G, H, Cavity 

Method

Link function                 Logit
Categorical predictor coding  (-1, 0, +1)
Rows used                     1440


Response Information

Variable   Value  Count
Deformato  1        203  (Event)
           0       1237
           Total   1440


Deviance Table

Source        DF  Adj Dev  Adj Mean  Chi-Square  P-Value
Regression    11    49.11    4.4642       49.11    0.000
  A            1     0.06    0.0607        0.06    0.805
  B            1     0.81    0.8073        0.81    0.369
  C            1     0.01    0.0067        0.01    0.935
  D            1     6.40    6.4016        6.40    0.011
  E            1    12.31   12.3116       12.31    0.000
  F            1     3.53    3.5258        3.53    0.060
  G            1     0.33    0.3267        0.33    0.568
  H            1     1.93    1.9269        1.93    0.165
  Cavity       3    24.30    8.0987       24.30    0.000
Error       1428  1122.26    0.7859
Total       1439  1171.37


Model Summary

Deviance   Deviance
    R-Sq  R-Sq(adj)      AIC
   4.19%      3.25%  1146.26


Coefficients

Term         Coef  SE Coef   VIF
Constant  -1.9165   0.0834
A         -0.0201   0.0817  1.00
B         -0.0734   0.0817  1.00
C         -0.0067   0.0817  1.00
D         -0.2073   0.0824  1.00
E          0.2884   0.0831  1.00
F         -0.1536   0.0820  1.00
G          0.0467   0.0817  1.00
H         -0.1135   0.0819  1.00
Cavity
  1        -0.660    0.164  1.79
  2         0.085    0.134  1.58
  3         0.468    0.124  1.54


Odds Ratios for Continuous Predictors

   Odds Ratio       95% CI
A      0.9801  (0.8351, 1.1502)
B      0.9292  (0.7917, 1.0907)
C      0.9933  (0.8464, 1.1657)
D      0.8128  (0.6916, 0.9552)
E      1.3343  (1.1338, 1.5703)
F      0.8576  (0.7302, 1.0072)
G      1.0478  (0.8928, 1.2297)
H      0.8927  (0.7604, 1.0481)


Odds Ratios for Categorical Predictors

Level A  Level B  Odds Ratio       95% CI
Cavity
  2      1            2.1046  (1.2849, 3.4474)
  3      1            3.0872  (1.9218, 4.9594)
  4      1            2.1530  (1.3162, 3.5218)
  3      2            1.4669  (0.9869, 2.1802)
  4      2            1.0230  (0.6736, 1.5536)
  4      3            0.6974  (0.4700, 1.0347)

Odds ratio for level A relative to level B


Regression Equation

P(1)  =  exp(Y')/(1 + exp(Y'))


Cavity
1       Y' = -2.576 - 0.02012 A - 0.07339 B - 0.006706 C - 0.2073 D + 0.2884 E - 0.1536 F
             + 0.04668 G - 0.1135 H

2       Y' = -1.832 - 0.02012 A - 0.07339 B - 0.006706 C - 0.2073 D + 0.2884 E - 0.1536 F
             + 0.04668 G - 0.1135 H

3       Y' = -1.449 - 0.02012 A - 0.07339 B - 0.006706 C - 0.2073 D + 0.2884 E - 0.1536 F
             + 0.04668 G - 0.1135 H

4       Y' = -1.809 - 0.02012 A - 0.07339 B - 0.006706 C - 0.2073 D + 0.2884 E - 0.1536 F
             + 0.04668 G - 0.1135 H


Goodness-of-Fit Tests

Test               DF  Chi-Square  P-Value
Deviance         1428     1122.26    1.000
Pearson          1428     1457.86    0.285
Hosmer-Lemeshow     8        8.31    0.403

Of course the model sucks, but How can I calculate the probability of event (Y=1) based on the two significative factors D and E? Something like which is the probability of Y=1 if D=1 and E=1, and if D=-1 and E=1,ecc.?

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1 Answer 1

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To make a prediction you will have to supply a value for all the fitted predictors. If you regard some predictors as negligible you could either refit omitting negligible predictors, or fix their values at the mean values from the calibration set. Either way, you will end up with an equation in the non-negligible predictors.

NOTES: a) Although F does not reach the "magic" p=0.05 personally I would not regard it as negligible. I'd think about including H as well,

b) Cavity has a substantial effect, so in Minitabs presentation you will have a separate equation for each cavity.

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  • $\begingroup$ Except for Cavity that has 4 levels (1 - 4) the factors are coded as -1/+1. But of course since is a codification, this -1 and +1 refer to some continuous values. Let’s suppose that this is my equation Y' = -2.576 - 0.2073 D + 0.2884 E - 0.1536 F how can I compute the probability of getting 1 with D=245, E=255 and F=1,2 ? Yes, you are right, F is borderline but H is pretty far away from the magic value ;) $\endgroup$
    – gmeroni
    Commented Nov 14, 2014 at 8:23
  • $\begingroup$ @gmeroni I don't understand your comment about factor coding. I guess this refers to the "8 continuous predictors" A:H, which Minitab would not usually refer to as factors. If you've used the Minitab (V17?) option to "Standardize continuous predictors: Specify low and high levels to code as -1 and +1" you'll need to allow for that, but the output you quote is not consistent with that coding. If you use that coding the coefficients table is headed Coded Coefficients, the regression equations are headed Regression Equation in Uncoded Units with different coefficients values from the table. $\endgroup$
    – user20637
    Commented Nov 17, 2014 at 12:49
  • $\begingroup$ @gmeroni If your equation is Y' = -2.576 - 0.2073 D + 0.2884 E - 0.1536 F and D=245, E=255 and F=1.2 (not 1,2) then Y' = -2.576 - 0.2073*245 + 0.2884*255 - 0.1536*1.2 = 19.99 and P(1) = exp(19.99)/(1+exp(19.99)) which is practically 1.0 $\endgroup$
    – user20637
    Commented Nov 17, 2014 at 12:50
  • 1
    $\begingroup$ @gmeroni With respect to omitting predictors, usually I don't like to do so. See Frank Harrell's comment at link. You have reason to believe - albeit not proof - that F and H contain useful predictive information. You may have reason to exclude them, but you haven't given any. $\endgroup$
    – user20637
    Commented Nov 17, 2014 at 12:57

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