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?
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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