Assumptions of Regression
There are five Assumptions of Regression
1. Linearity
2. Normality
3. No Multicollinearity
4. No Auto-correlation
5. Homoscedasticity
Linear Relationship:
For looking at linear relationships, it's easy to draw a scatter plot between the dependent variable and the independent variable.
Look at this scatter plot. Here the data points align more like a straight line. So here we can say there is a linear relationship between variables. I will explain how to create a scatter plot in my next video. If you get a scatter plot similar to this plot, you can say there is a linear relationship between the dependent variable and the independent variable.
Look at this one. The data points are not like straight lines. Therefore, this one is a non-linear one.
Normality:
Let's move on to normality.
You have to determine if the data set is normally distributed or not.There are two ways that can determine whether data is normally distributed or not.
Analytical way and graphical way.
You can use Kolmogorov-shimirnov test and Shapiro-wilk test as analytical method and you can use histogram or QQ plot as graphical method.
The histogram and QQ PLOT are the simplest ways to determine whether your data is normally distributed or not.
Multicollinearity:
The next one is multicollinearity.
Multicollinearity is a statistical concept where several independent variables in a model are correlated.
To identify multicollinearity, you have to calculate the variance inflation factor (VIF) and tolerance.
Using these formulas, we can calculate VIF and tolerance. If the VIF value is greater than 10, it means there is mullticolinearity. If the tolerance value is less than 0.1, it indicates there is mullticolinearity between independent variables.
Auto-correlation:
The next one is autocorrelation. The easiest way to determine if there is autocorrelation or not is to use the Durbin-Watson test.
The Hypotheses for the Durbin Watson test are here.
H0 = no first order autocorrelation.
H1 = first order correlation exists.
If you want to know how to perform the Durbin-Watson test, Go and watch my other videos.
Homoscedasticity:
The next one is homoscedasticity. What is Homoscedasticity? In regression analysis , homoscedasticity means a situation in which the variance of the dependent variable is the same for all the data.
What is heteroscedasticity ? Heteroscedasticity refers to data for which the variance of the dependent variable is unequal across the range of independent variables.
For determine homoscedasticity, you can use Breuch-pegan test.
These are the hypothesis for breuch pegan test.
H0 = there is constant variance or homoscedasticity in residual.
H1 = there is not constant variance or homoscedasticity in residual.
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