# Regression Analysis

Regression Analysis is used for finding out the relationship between a dependent variable and one or more than one independent variable. The functional relationship between the dependent variable & independent variable is called the regression equation.

Linear Regression

If the relation between dependent and independent variable is linear then it called linear regression and the graph is called curve regression. If the curve is a straight line then it called a line of regression.

If more than one independent variable is there then it called multiple regression. The Independent variable also called the regressors and the dependent variable called the response variable.

### Regression Analysis Aim

Aim of the regression model is to find out estimates as best as possible, based on the dependent variable and independent variable. In theoretical notation usually taken Y as the dependent variable and X as the independent variable and line regression are X on Y.

### Regression Analysis Assumptions

There are few assumptions in the linear regression model.

The variables X and Y are normally distributed. The assumption of normality becomes essential while testing the significance of regression parameters or finding their confidence limits.

The population value of Y corresponding to each X has a mean µ which lies on the line µ=β0+β1x

The variable X is measured without error and homoscedasticity.

What is the regression coefficient?

The regression coefficient β is a measure of change independent variable Y corresponding to a unit change in Independent variable X.

Sir Francis Galton named the term regression for relation between two variables.

How to test the significance of the regression coefficients?

The significance of the regression coefficient can be tested by students t-test with (n-2) degrees of freedom.

Why we need regression analysis?

1) In some cases, dependent variable Y cannot be measured directly in such cases with the help of an independent variable we can measure it.

2) The effect of certain treatments can better be adjusted by estimating the effect of concomitant variables.

3) The length of confidence can reduce the basis while using dummy variables.

4) Regression equation used for prediction purposes.

5) To measure the effect of the independent variable.

## Nonlinear Regression

If the regression line is not linear then it’s called nonlinear regression.

The following equations are the most important in nonlinear regression.

1) The second-degree curve of a parabola

2) Exponential growth curve

3) Exponential decay mode

4) Logistic Growth

5) Compertz function

6) Mitscscherlich function

7) Cubic Parabola

8) Equilateral Hyperbola