13th September 2023- Wednesday class

In today class, I have learnt a new topic called P-value which is a probability of a null hypothesis to be true. Null hypothesis (H0)states that there is no relationship between variables. Alternative hypothesis(H1) states that there is a relationship between variables. The significant p -value is 0.05. For example, when we toss a coin the probability for a tail to occur is 0.5 and for a head to occur is 0.5. Let’s assume the null hypothesis H0 – The coin is fair and H1 – The coin is not fair. If we toss a coin for 20 times and everytime we get a tail then the value of p goes on decreasing which means there is something tricky or wrong in that case we should reject the null hypothesis.  If the value of p is equal to significant value 0.05 then we can confirm the null hypothesis and state that coin is fair.

In previous class, I was confused about heteroscedasticity but today what i understood is heteroscedasticity is a condition where the data points keep fanning out from the best fit line (or) error or residual increases as the value of variable increases. In simple terms, heteroscedasticity occurs when there is huge difference between actual value and predicted value.  This a visual way of finding heteroscedasticity present in the model. In statistical way we use Breusch-Pagan test to detects the presence of heteroscedasticity in the linear regression model. This test uses null and alternative hypothesis.

Steps to perform Breusch – Pagan test

1. Fit the linear regression model and detect the residuals.

2.Calculate the squared residuals (R*2) of the regression model.

3. Now fit a new linear regression model using the response values of R*2 (R-Squared).

4.Calculate the Chi Square test as nr*2

where n is total number of observations and r*2 is R-sqaured of new linear regression model.

If the value of p is less than 0.05 then we reject the null hypothesis and state that heteroscedasticity is present, if not it fail to reject the null hypothesis and states that homoscedasticity is present.