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MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 4: Logistic Regression, Indian Institute Of Technology Kanpur, Mathematical Optimization

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rosi10agarwal
6 Apr 2023
School
Indian Institute of Technology - IIT Kanpur
Department
Mathematics
Course
MTH-416, REGRESSION ANALYSIS
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Document Summary

The log-link function is x i ln( x i g i i i i i g. Note that in identity link function, the predicted values of y can be negative but in log-link function, the predicted values of y are nonnegative. We use the method of maximum likelihood estimation to estimate the parameters of the poisson regression model. The likelihood function is based on poisson distribution with parameter and then. " s are estimated through the link function. The likelihood function of y is y y. 1 i p y i i exp( i i n i. 1 i y i i i y i exp y i n. L y n ln( i y i n n i ln( y i. " s through the link function i can be related to. 1 i y i x i g exp( 1 g x i x x i x .

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For this exercise, round all regression parameters to three decimal places. The following table shows the number†P of design patents awarded by the U.S. Patent and Trademark Office from 1950 through 2010. t = years since 1950 P = patents

0= 4718

10=2543

20=3214

30=3949

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50=17,413

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