By Sharath Kumar Aitha. Instructor: Dr. Dongchul Kim.

 Introduction.  Logistic Regression.  Formula  Conditional Density Function.  Maximum log like hood  Pseudo code  Classification  Output  Application  Conclusion

 To analyze the historical data of online shop customer behaviors by logistic predictive modeling and predicts whether the customers purchase a tablet pc online shop.  Analyzes data by datamining and establishes predictive modeling based on logistic regression.

 This is the most commonly used technology used for developing predictive modeling.  Its function is to look for a variety of equations which reflects the customer behavior patterns according to the observations of X and Y.  There are two types of regressions they are: 1.Ordinary least square Regression(OLS) 2.Logistic Regression.

 If the variable Y is continuous we usually use OLS  For example if variable Y is the sales volume of tablet PCs and the distribution of these observations is more beautiful, we can use OLS.  But the requirements of OLS of Y are very harsh and difficulty, so we use logistic regression.

 Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome.  This is a unsupervised function where we need to provide the input values.

 If we have feature data t i ∈ℜ and label data y i ∈ {0,1},i = 1,2,···,n. corresponding to two classes. we can use logistic regression to solve this by doing regression between y and t on logistic function  H(t)=1/1+e -(at-b)  T is the input.  E is the exponential  A is the coefficient to adjust the slope.  B is the parameter.

 Def: Suppose X and Y are continuous random variables with joint probability density function f(x,y) and marginal probability density functions f X (x) and f Y (y), respectively. Then, the conditional probability density function of Y given X = x is defined as: provided f X (x) > 0.  Formula: conditional density function p(y/t):  P(y/t)=h(t) y (1-h(t)) (1-y)  Which can also be written as  P(y/t)=(1/1+e -(at-b) ) y (1/1+e (at-b) ) (1-y)

 This is a statistical method used for estimating the co- efficients of a model.  The likelihood function measures the probability of observing the particular set of dependent variable values that occurs in the sample.

Algorithm 1 One dimension logistic regression Input: t; y Output: a; b 1: Initialize a and b 2: repeat 3: a = a + τ ∂ℓ/∂a 4: b = b + τ ∂ℓ/∂b 5: until convergence of a and b

 ∂ℓ/∂a  ∂ℓ/∂b

 For a testing data given feature t or x, by Eq.(1), we get h, it is the probability of y=1. so the discriminant function is:

Design and implementation:

 Logistic Regression modeling can be used in predicting the possibility of a customer to buy a commodity.  This is also helpful for the online shop owner to make the decision.