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Definition: Linear and Logistics Model
They are models used in regression analysis in order to predict an outcome of a dependent variable from one or more independent variables, for explicit prediction and causality analysis and exploring relationships and asses contributions.
In the traditional linear regression model, both the dependent and independent variables are continuous or ordinal. There is a single dependent variable. There could be single or multiple independent variables. The general form of the regression equation is given as:
Y = b0 + ∑ bi xi + ɛ
Where ɛ is the error term.
Logistic regression is another generalized linear model procedure that is used for regression analysis, but in this case the dependent variable is categorical while the independent variables are continuous, i.e. the equation is regressing for the probability that the outcome would be one of the two binary states 0 or 1.
The equation for the probability of Y=1 is given as,
P(Y=1) = 1/ 1+ e- (b0 + ∑ bi xi)
To give an example, if you want to measure how a BMI predicts the blood cholesterol levels, linear regression would be used. However, to predict the odds of being a diabetic using BMI, logistic regression would be used.