Implementation of the Logistic Regression Model and its Applications

The purpose of an analysis using this method is the same as that of any technique in constructing models in statistics, namely to find the best and most reasonable model to describe the relationship between a result variable and a set of variables independent. We are interested in how the costs affect them and if a customer has a travel card. 
Credit card customers are shown to be 6 times more likely to use it regardless of the cost they make.It is also shown that a customer is more likely to use a travel card when costs increase Through logistic regression, which gives the probability that a result is an exponential function of the independent variables, we will see how through our data we will come to very important conclusions.


Introduction
Regression methods have been an integral part of any analysis of data related to the description of the relationship between a response variable and one or more explanatory variables. Logistic regression model is a form of regression which is used when the dependent variable (Y) is dichotomous (binary) and qualitative values i.e., 2 levels e.g., with or without customer card, etc., and the independent variable (X s) can be numerical, categorical or mixed. This technique is applied in different research area, particularly in the medicine (e.g., Antonogeorgos G. et al., 2009), socio-logical sciences (e.g., HL Chuang, 1997) and in the education (state graduation results) (e.g., Sadri Alija, et al., 2011, Muca M., et al., 2013.
The purpose of an analysis that uses this method is the same as that of any technical building models in statistics, so to find the best and more reasonable model to describe the connection between a variable result and a set of variables independent. In logistic regression after adjusting the model, the emphasis is to evaluate and interpret is o the coefficients and their values, where conformity assessment methods are more of a technical nature.
variable Y is qualitative (binary) with two values or categorical with more than two values and the independent variables can be quantitative, qualitative or mix. In multiple regression analysis, the mean or the expected value of y, E(Y), is calculated from equation (1) While, in the logistic regression is shown (Chao-Ying Joanne Peng and Tak If the dependent variable y is coded as 0 and 1, the value of E(y) in equation (2) provides the probability that y = 1 given a particular set of values for the independent variables (3)

Data. Linear regression analysis logistics LR
It is believed that the total costs in a supermarket and the fact that a customer has a credit card or not, are two important variables in predicting if a client who has client card will use it. Therefore, in this study we used a sample which consists of information for n = 100 clients (50 have travel card and a travel card 50 have not). The set of data consists of a dependent variables and forecast variables (predictor variables). For every customer the total costs marked 1000 ALL and {0,1} are listed whether or not the customer has credit card (see Table 1). Logistic regression model will be used to assess what kind of potential customer is to benefit from the promotion of the company. Use credit card {0 → don't use and 1 → use} Figure 1, shows that customers can be grouped as follows: • Customers who do not use travel cards (78%, 39 from 50) spend less (to 10 thousand) than those who buy with credit card.

Logistic Regression Analysis
The linear logistic regression model was adapted into the set of the data presented in Table 1. In Table 2 are represented the results of RL method performed in SPSS.
According to the model, the natural logarithm of odds that a client use client card is positively associated with both variables (cost and Credit card) with p = .467 and p = .001 respectively. In other words, more money a client has spent, the greater will be the chance of being a user (that a client used client cart). Exp(B) for the total cost (expenditure) is equal to 1.036, which means when the total costs are added to a unit (1000 ALL), the client is 1.036 times more likely to use the card customer than not, or if the difference in domestic currency (ALL) is 20 thousand then a client is 2.03 = 1.036 20 times more likely to use the travel card. Customers who use credit cards are more likely to use client card compares to they that not have travel card because credit card customers are codified 1 while customers who have no credit card are codified with 0. Actually, the odds ratio for clients with a travel card (odds) who use the customers card is 6.015 (=e 1.794 Table 2) times greater than the odds ratio for customers who have no credit card. Also based on the 95% confidence interval for the expenditure we see that it contains the value 1 and in such cases it is said that change in expenditures is statistically insignificant, and for other intervals that do not contain the value 1 the opposite is true.

Table 2. Results of the logistic regression analysis
We can now use equation (4) to estimate the probability of using the customer card for a particular type of customer. Thus, for this group of customers, the probabilities of using or not using the customer card when his total expenses are equality as some numerical indicators (minimum, maximum, mode, and the average costs) are shown in Table 3.
As you can see the tables display in SPSS works by steps, where in the zero interation we see that the tables are simplified because they do not yet take into account the data I modify in the respective windows, and the first interation includes all details as a result of tacing into account data from windows that SPSS extracts.

Binary logistic regression interpretation (binary logistic regression)
In Table 4 are shown the ratios of two conditional probability (equation 8) for customers using the customer card when the total of her expenses as some numerical indicator (minimum, maximum, mode, and the average cost).

Table 4. Assessment report two conditional probability by some numerical characteristics
The multiple logistic regression model has the form (1) The cut v alue is .500 b.

1.
If the response is binary, then the error terms can take on two values, namely, Because the errors is dicreate, normaly assuption is violated.

2.
The error variance is not constant and it can be seen that it is a function of probabilities, because The interpretation of  s is rendered using either the odds ratio (for categorical predictors) or the delta-p (for continuous predictors). The null hypothesis states that all  s equal zero. A rejection of this null hypothesis implies that at least one of the parameters does not equal zero in the popullation, which means that the logistic regression model predicts the probability of the answer better than the mean of the answer Y (see Item 2 to some problems encountered in linear model) that determined by draw (2).

Conclusions
The analysis showed that customers who use credit cards are more favorable to use customers card compared to those who don't have credit card and the chances increase when total cost rise. Also, it is seen that a credit card customer is 6 times more favorable to use the customer card compared to those who don't have customer card.