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[Audio] Our today video topic is " Logistic Regression" We will discuss definition, examp[les, objectives etc.

[Audio] Definition Special form of regression in which the dependent variable is nonmetric, dichotomous (binary) variable..

[Audio] Let us discuss an example to understand logistic regression in a better way Suppose we want to study the labor force participation (LFP) decision of adult males. Since an adult is either in the labor force or not, LFP is a yes or no decision. Hence, the response variable, or dependent variable, can take only two values, say, 1 if the person is in the labor force and 0 if he is not. In other words, the dependent variable is a binary, or dichotomous, variable. Labor economics research suggests that the LFP decision is a function of the unemployment rate, average wage rate, education, family income, etc. we do not have to restrict our response variable to binary variables only (two categories). It may be multiple-categories..

[Audio] Main objectives of logistic regression are 1. Identify the independent variables that impact group membership in the dependent variable. 2. Establishing classification system based on the logistic model for determining group membership..

[Audio] Now the next question which emerged after some little study Why we use logistic instead the discriminant? The answer to this question is When our data is from multivariate normal distribution we prefer to discriminant analysis. If this case is violated we tend to logistic regression..

[Audio] Now there are some assumptions to keep in mind while using logistic regression. 1. It does not require any specific distributional form of the independent variables. 2. It does not require linear relationship between the independent variables and the dependent variables as does multiple regression. 3. However binary logistic regression requires the dependent variable to be binary and ordinal logistic regression requires the dependent variable to be ordinal.

[Audio] Now we will discuss various areas in which logistic regression is used. Medical field 2. Engineering 3. Marketing 4. Economics 5. Social sciences.

[Audio] Logistic regression contain 1. Causal relationship 2. Medically: Do body weight, calorie intake fate intake and age have an influence on heart attack...? 3. Biologically: Does the herbicides and oxygen level in water kill the plants..? 4. Management: Do customer satisfaction, brand perception, price perception influence the purchase decision..? 5. Forecasting 6. Will a subject who smokes X cigarettes a day and works Y hours get lung cancer?.

[Audio] The Probit Model If we choose the normal distribution as the appropriate probability distribution, than we can use the probit model..

Yi =βo+ β1X or Ii = βo+ β1X. where I is known as unobservable utility index(a latent variable)..

[Audio] Example Consider a home ownership example. Suppose Y=1 a family own a house and Y=0 it does not. The decision that ith family own a house or not depends upon an unobservable utility index Ii(the latent variable)that is determined by one or more explanatory variables, say income Xi,in such a way that larger the value of the index the greater is the probability of a family owning a house..

[Audio] For this example our logic model will be Ii = βo+ β1Xi Where Xi is the income of the ith family. Now it is reasonable to assume that there is a critical level of the index, call it Ii *, such that if Ii exceeds Ii * the family will own a house otherwise it will not..

Explanation. Subscribe.

Zi is the Stander normal vaiable. F is the stander normal CDF. P is the probability that an event will occur. The CDF of Normal Distribution is given by F(x) = fx_0æe-7 dz Replace X with latent variable F(li) = f!'oo d ß1+ß2Xi - F(li) = f-00.

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