An Introduction to Logistic Regression. Eni sumarminingsih , Ssi , mm Program studi statistika Jurusan matematika Universitas brawijaya. Outline. Introduction and Description Some Potential Problems and Solutions. Introduction and Description. Why use logistic regression?
An Introduction to Logistic Regression
Enisumarminingsih, Ssi, mm
In the OLS regression:
Y = + X + e ; where Y = (0, 1)
You are a researcher who is interested in understanding the effect of smoking and weight upon resting pulse rate. Because you have categorized the response-pulse rate-into low and high, a binary logistic regression analysis is appropriate to investigate the effects of smoking and weight upon pulse rate.
Regression Analysis: Tekanan Darah versus Weight, Merokok
The regression equation is
Tekanan Darah = 0.745 - 0.00392 Weight + 0.210 Merokok
Predictor Coef SE Coef T P
Constant 0.7449 0.2715 2.74 0.007
Weight -0.003925 0.001876 -2.09 0.039
Merokok 0.20989 0.09626 2.18 0.032
S = 0.416246 R-Sq = 7.9% R-Sq(adj) = 5.8%
Predicted Values outside the 0,1 range
Descriptive Statistics: FITS1
Variable N N* Mean StDev Minimum Q1 Median Q3 Maximum
FITS1 92 0 0.2391 0.1204 -0.0989 0.1562 0.2347 0.3132 0.5309
The "logit" model solves these problems:ln[p/(1-p)] = + X + e
The slope coefficient () is interpreted as the rate of change in the "log odds" as X changes … not very useful.
exp() is the effect of the independent variable on the "odds ratio"
Logistic Regression Table
Odds 95% CI
Predictor Coef SE Coef Z P Ratio Lower Upper
Constant -1.98717 1.67930 -1.18 0.237
Yes -1.19297 0.552980 -2.16 0.031 0.30 0.10 0.90
Weight 0.0250226 0.0122551 2.04 0.041 1.03 1.00 1.05
Goodness-of-Fit Tests displays Pearson, deviance, and Hosmer-Lemeshow goodness-of-fit tests. If the p-value is less than your accepted α-level, the test would reject the null hypothesis of an adequate fit.
The goodness-of-fit tests, with p-values ranging from 0.312 to 0.724, indicate that there is insufficient evidence to claim that the model does not fit the data adequately