Logistic Regression[1]

Survey Study of the Requirements Of a Teller Machine Within the University Premises For the Public Usage.

What is Regression. Linear Regression Methods. Logistic Regression. Survey Study of the Requirements Of a Teller Machine. Analysis results by using mathematical methods. Conclusion.

Regression Analysis v Regression analysis is a statistical technique used to describe relationships among variables. vSimple linear regression vMultiple linear regression vLogistic regression

The General Linear Model v If the relationship between y and x is believed linear, then the equation expressing this relationship is the equation for a line ,

v represent the yintercept, the point where the line crosses the vertical (y) axis, and represent the slope of the line. v The simplest case to examine is one in which a variable y, referred to as the dependent variable, may be related to another variable x, called an independent or explanatory variable. Ø Example: For accounting, total cost = fixed cost + Variable cost

Example of population Regression lines

v The equation of this line is written as ,

v Where, - is the conditional mean of y given a value of x, - is the y intercept for the population regression line, - is the slope of the population regression line.

v For example: Suppose that we are developing a model to describe the temperature of the water off the continental shelf. Science the temperature depends in part on the depth of the water, two variables are involved. These are, x-The water depth (independent variable) y-The water temperature (dependent variable) we want to describe the behavior of the water temperatureunder the assumption that the depth of the water is known precisely in advance. v Even if the depth of the water is fixed at some

v For example , if several temperature measurements are taken at various places each at a depth of x=1000 feet, these measurements will vary in value. For this reason, we must admit that for a given x, we are really really dealing with a “Conditional ” random variable, which denoted by Y|x (Y given that X=x). v

- The conditional mean of y given a value of x

v We present our x values at =3000......

= 1000,

=2000

=5000 feet.

v Regardless of how the X values for our study are selected, Our random sample is properly viewed as taking form,

Multiple Linear Regression v The General Linear Model:

v v

- denote the known real numbers - denote the unknown real numbers

Polynomial Model of Degree p v The general polynomial regression model of degree

pexpresses the mean of the response variable Y as a polynomial function of one predictor variable X,

v Where p is a positive integer If we let ,

v Quadratic model:

v Cubic model:

Why use Logistic Regression Rather Than Ordinary Linear Regression In early satiations use ordinary linear regression for there data analysis. Statistic develop day by day, however, are now most satiations & psychologists use logistic regression. v The outcome variable is binary or dichotomous. v One of the assumptions of regression is that the variance of Y is constant be the case with a binary variable , become the variance is PQ. Ex: When the 50 percent of the people are, then variance is 0.25. It’s maximum value as we move more extreme value, the variance decreases, when P=0.1, the variance is 0.1*0.9=0.09, so as P approaches 1 or zero, the variance approaches zero.

The General Linear Model v If the relationship between y and x is believed linear, then the equation expressing this relationship is the equation for a line ,

v represent the y intercept, v the point

where the line crosses the vertical (y)

axis, v

- represent the slope of the line.

v

- represent error term so y & x also distributed normally.

v If y distributed another distribution (Binomial, Poison). so we wont to go to another method.

Scatter Plot of CHD by AGE for 100 Subjects

The Percentage of subject with CHD

Plot of The Percentage of subject with CHD in Each Age Group

The Simple Logistic Model Logistic regression is a mathematical molding approach that can be use to describe the relationship of several variable X to a dichotomous dependent variable Y. v where Y is typically called as 1 or 0 for its two possible categories. v The logistic model describes the expected value of Y (i.e. E(Y ) ) in terms of following “logistic formula”. v

----(1)

v For (0, 1) random variable such as Y . It follows from basic statistical principals about expected values that E(Y ) is equivalent to probability Pr(Y = 1) for a (0, 1) random variable Y , E(Y |x) = 0*Pr(Y=0)+1*Pr(Y=1)= Pr(Y = 1) -----(2)

Pr(Y = 1) =

------(3)

v In order to simplify notation, we use the quantity, -----(4) By equation (3) & (4)

v A transformation of that is central to my study of logistic regression is the logistic transformation. v This transformation is defined, in terms of ------ (6) By equation (5) & (6)

----(7)

Multiple Logistic Regression Model v Consider a collection of p independent variables denoted by the vector X=(x1, x2, x3...., xp). v The logit of the multiple logistic regression model is, ----(1)

v Then logistic model is, -----------(2)

v In general, if a nominal scaled variable has k possible values, then k-1 design variables will be needed. v since, unless stated other wise, all of our models have constant term. v The design variables will be denoted as and the coefficients for these design variable will be denoted as v Thus, the logit for a model will p variables and variable being discrete would be,

example: v one of the independent variable is race. v Which has been coded as White, Black, and Others.

v One possible coding strategy is that when the respondent is White, The two design variables, D1 and D2, would both be set equal to zero. v when represent is Black , D1and D2, would both be

v (1) White

v (2) Black

v (3)Other

Model-Building Strategies And Methods For Logistic Regression

v The goal of any method is to select those variables that result in a best model within the scientific context of the problem. In order to achieve this goal we must have: (1) A basic plan for selecting the variables for the model (2) A set of methods for assessing the adequacy of the model both in terms of its individual variables and its overall fit.

Variable selection v There are several steps one can be follow to aid in the selection of variables. v The process of model building is quite similar to the one used in linear regression. vCheek the variables are continuous ,categorical or dummy variable. vSelect only dummy variables. vCheek P-values. (0.25 level) vUse stepwise methods for select variables.

P-values v Cheek p-values. ( p-value > 0.25.) v Once the variable have been identified, we begin with a model containing all of the selected variables. v Our recommendation that selection is based on the work by Bendel and Afifi (1977) on linear regression and on the work by Mickey and Greenland (1989) on logistic regression. v Thus we can show that use of more traditional level (such as 0.05 level) often fails to identify variables known to be important.

stepwise procedure. v There are two main versions of the step wise procedure. (a) Forward selection with a test for backward estimation (b) Backward elimination followed by a test for forward selection

Survey Study of the Requirements Of a Teller Machine Within the University Premises For

v The goal of this study to survey study of the requirement of a teller machine with in the university premises for the public usage. v We prepared to questionnaires for collect data and interview more than 500 people around the university area in wellamadama.

v premises comprising vacademic, vnon academic staff, vinternal & external student and

University Population v Academic staff v Non Academic staff v Internal student v External student

Size of The University Population

Size of the population

Academic

6000 Temp &Demo

5109

5000

Non Academic

4000 3000

Security

2000 1000 0

185 Academic

110

399

704 45

Temp Non Security &Demo Academic

Internal student

External student

Internal student External student

Academic Staff of The University v Lecturers v Temporary & Demonstrate staff

Lecturers Staff of The University

Academic staff

H&SS

5% 44%

36%

Management

Scinance 15% Fisheries

Demonstrate Staff

Temparary & Demostrete staff 80 70

H&SS

75

60

Management

50 40 30 20 10 0

Scinance

17

13 5

H&SS ManagementScinance Fisheries

Fisheries

Non Academic Staff v Administrative officers v Clerical staff v Technical officers v Minor and other staff members

Non Academic Staff

Non academic staff

5% 1%

11%

1%

Administrate H&SS Management Scinance

33% 49%

Fisheries Total

Owns a Savings Account

No.of saving accounts for the sample taken out of university premises 3%

Yes No

97%

Analysis of Having Accounts For the Sample Taken Out

Living Places in the Sample Who Haven’t Serving’s Accounts.

University Staff & Student Maintain Their Accounts With

Analysis of University Staff &

Number of Accounts Obtains in University Banks.

How the Money of Payments Divided Each of the

Number of Accounts Obtains in University Banks .

How the of Payments Divided Each of

v academics belong to the highest salary scale writhing the university community. v The Bank Of Ceylon is experiencing a great loss of income due to the fact that academic accounts. v Therefore, the bank of Ceylon can increase their profit if they recover the academics trust on their bank.

Sample Members Have Obtain Teller Facility.

Analysis of Members Teller Facility.

Where They Have There Teller Facility

v Students mostly use the teller machine during evenings, v attacked by the village boys. v Also some robberies for withdrawn money

v Close to the Matara - Kataragama road, many outsiders also Used it. v students who have come from north and eastern areas are suspicious of leaving the university premises to the external teller machine in evenings because they may be questioned by either villagers or security persons. v I suggest to establish teller machine within the

Number of Teller Machine to be Within or

New Teller Machine to be Within or Outside in According to the above graphs, it is clear that most of them need the installation of a teller machine within the university premises, and lots of reasons are behind this. v It is very convenient to retrieve money. v It saves time. v High security.

The Number of Customers Who Are Interested to New Teller Machine.

Results v The goal of the analysis was to identify, vwho were interested for ATM facility for university premises, vwhy were they interest for this facilities.

v The variable PLACE was treated as a categorical variable in the regression analysis, v so three dummy variable had to distinguish the four places they are living. v Place of Inside the Matara area (PLMA) v Hostel in side University (PLOM) v living Outside the Matara area (PLIUH) v Hostel out side University (PLOUH)

v Also The variable ID was treated as a categorical variable. v So dummy variable had to distinguish the four sections where the members are working. v ID-Student (IDS) v ID-Non academic (IDNA) v ID-Academic (IDA) v ID-Temporary Academic (IDTA)

Logit Form Of The Model v The logit from of the model being fit given as, logit[Pr(Y = 1)] =

v Where, Y denotes the depend variable INTEREST. v The results of fitting the univariable logistic regression models to these data are given in result Table.

v Using the given table, we now focus on the information provided under the heading Analysis of Maximum likelihood estimators from this information, we can see that the ML coefficients obtained for the fitted model are,

v So that fitted model is given (in logit form) by,

v Based on this fitted model and computer output, we can compute the estimated vp- value vodds ratio for finding factors of interesting the ATM machine within the university premises for the public usage. v We do this using the Forward selection with a test for backward estimation. v With the exception of GENDER there is evidence

New Reduced Model v The results in Table 2, when compared to Table 1, indicate weaker associations for some covariates when controlling for other variables. v The new reduced model is written in logit from as, logit[Pr(Y = 1)] =

v By using the computer output we can see that the ML coefficients obtained for the new fitted model are,

v So that fitted model is given (in logit form) by,

v Then we can define logistic function,

.

v The logit transformation is given by,

v By using the previous results, we can substituted the values for logistic transformation,

example: v one of the independent variable is identification code. v Which has been coded as Academic, Nonacademic, Demonstrate staff and Students. v Student is a base group.

v Students

v Nonacademic Staff

v Academic Staff

v Demonstrate Staff

v Students

v Nonacademic Staff

v Academic Staff

v Demonstrate Staff

Differences of Interesting from identification code.

1-Demostrate staff 2-Student 3-Academic 4-Non academic

Conclusion v Compared with the other subjects, the non academic staff (IDNA) were interested in more than three times to the requirement of a Teller machine facility. (OR= 2.52 & C.I= 1.21 to 5.24) v Also the current account owners in Bank Of Ceylon were interested more than 5 times. (OR= 4.61 & C.I 2.46 to 8.63) v Academic staff & Students are also interested. v Temporary and Demonstrate staff were interested more than three times less for the requirement of this BOC teller machine (OR=0.33 & CI=0.17 to 0.66). v I suggest to establish a teller machine at the

Thank You.