DIFFERENCE BETWEEN LINEAR REGRESSION AND LOGISTIC REGRESSION
Regression is a statistical technique to investigate relationship between dependent variable and independent variables which can be linear, nonlinear.
logistic regression is statistical technique to investigate relationship between ordinal dependent variable and independent variables. logistics regression can be multinomial if there are more then two ordinal dependent variable.
1. Variable Type : Linear regression requires the dependent variable to be continuous i.e. numeric values (no categories or groups).
While Binary logistic regression requires the dependent variable to be binary - two categories only (0/1). Multinominal or ordinary logistic regression can have dependent variable with more than two categories.
2. Algorithm : Linear regression is based on least square estimation which says regression coefficients should be chosen in such a way that it minimizes the sum of the squared distances of each observed response to its fitted value.
While logistic regression is based on Maximum Likelihood Estimation which says coefficients should be chosen in such a way that it maximizes the Probability of Y given X (likelihood). With ML, the computer uses different "iterations" in which it tries different solutions until it gets the maximum likelihood estimates.
While logistic regression is based on Maximum Likelihood Estimation which says coefficients should be chosen in such a way that it maximizes the Probability of Y given X (likelihood). With ML, the computer uses different "iterations" in which it tries different solutions until it gets the maximum likelihood estimates.
3. Equation :
Multiple Regression Equation :
Multiple Regression Equation :
Logistic Regression Equation :
4. Curve :
Multiple Regression Equation : Straight line
4. Linear Relationship : Linear regression needs a linear relationship between the dependent and independent variables. While logistic regression does not need a linear relationship between the dependent and independent variables.
5. Normality of Residual : Linear regression requires error term should be normally distributed. While logistic regression does not require error term should be normally distributed.
6. Homoscedasticity : Linear regression assumes that residuals are approximately equal for all predicted dependent variable values. While Logistic regression does not need residuals to be equal for each level of the predicted dependent variable values.
7. Sample Size : Linear regression requires 5 cases per independent variable in the analysis.While logistic regression needs at least 10 events per independent variable.
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