# 95% confidence for simple logistic regression

I am generating and analyzing logistic regression models using MATLAB's fitglm. http://www.mathworks.com/help/stats/fitglm.html The fit models can then be visualized using plotSlice(glm). This figure is great, but is hard to customize.

I want to recreate the confidence bounds from plotSlice, but I am unable to. No where in documentation or figure can find the confidence bound data or the equation used to calculate it.

I have tried to recreate the bounds by calculating the variance of the sums of the fit coefficient variance as instructed in "Wiley Series in Probability and Statistics : Applied Logistic Regression (3rd Edition)"

Ex (1 parameter(B1) with intercept(B0)).

Var(g(xi)) = var(B0)+xi^2(var(B1))+2*(covar(B0,B1)) %the variance of the model at xi


where Var(g(xi)) is variance at xi, B0 is the fit intercept, B1 is the fit slope, xi is ith predictor value;

g_CI = +- z*sqrt(Var(g(xi)))% bounds at xi


where g_CI is 95% CI at xi, z is the z score from standard normal dist.

In MATLAB:

mdlCoeff =  [-1.2631;0.1558];
stats.se = [0.4472;0.0641];
stats.covb = [0.2000,-0.0271;-0.0271,0.0041];
testX = 7;
testp = mdlCoeff(1) + mdlCoeff(2)*testX;
phattest = exp(testp)./(1 + exp(testp));
varXitest = (stats.se(1).^2)+((testX.^2).*stats.se(2).^2)+(2*testX.*stats.covb(3));
phat_bounds3test = [phattest + (normcdf(.975).*(varXitest.^0.5)),
phattest - (normcdf(.975).*(varXitest.^0.5))]


this gives me 95% bounds of 0.5896 and 0.3333.

However, the plotSlice produce figure returns .5467 and .3700. Even when I reduce my z value 0 I don't get this narrow of a bound. Therefore I must be calculating varXitest incorrectly.

What am I missing here?

• Just a very general comment. Systems built for statistics such as R make such tasks far easier. Nov 8, 2015 at 17:03
• Thank you for your comment. Unfortunately this regression is part a large, many functioned program and switching to R would require a lot of work. Nov 8, 2015 at 17:04

testp = the estimated linear combination of X values