
Shameem Cholera introduces this econometrics course, highlighting common mistakes in simple linear regression and the confusion points to avoid to prevent errors on the final exam.
identify common mistakes in placing the error term in population and sample regression equations, clarifying that the population regression line has no error term while the sample equations include one.
Minimize the residual sum of squares in ordinary least squares, i.e., the sum of squared residuals, rather than the square of the sum of residuals (R.S.S. or S.S.E.).
Explore mistakes in simplifying mathematical expressions in simple linear regression, showing when removing X bar or deviations is valid and why the sum of deviations from the mean equals zero.
Explain that assumptions apply to the population error, not the sample error; define sample error as actual y minus fitted y_hat, using these notations.
Master the assumptions and their linkages in simple linear regression, using two-variable scatter plots to visualize how violations affect blue (best linear unbiased estimates) and hypothesis testing.
Distinguish standard deviation from standard error of beta hat in linear regression and explain why sigma squared is unknown, using residual sum of squares to derive the standard error.
This lecture highlights a common mistake in hypothesis testing for simple linear regression: formulating nulls about estimates, not population parameters, and shows the correct test statistic using intercept and slope.
The purpose of this econometrics course is to share with you the confusion points and some of the silly mistakes that students do while studying Simple Linear Regression.
Mistake 1: Placement of error term in population & sample regression equations. Also, have you ever seen 'X hat' in any of the regression equations?
Mistake 2: What is it that we minimise in the method of OLS?
Do you first sum the sample errors and then square the sum?
OR
Do you first square the sample errors and then take the sum?
Mistake 3: Not practicing the mathematical expressions. There are multiple ways of writing the formula for 'B2 hat'. Do you know all of them?
Mistake 4: You must have encountered some assumptions while studying Simple Linear Regression. Do you put the assumptions on the sample error? Also, what is the mathematical expression for the sample error?
Mistake 5: Not paying enough attention to the assumptions and linkages.
Example: What do you think about the following two statements? True or False.
Statement 1: In the presence of heteroscedasticity, the OLS estimators are biased.
Statement 2: For OLS estimators to be BLUE, the population error should follow a normal distribution.
Mistake 6: Standard Deviation OR Standard Errors?
Mistake 7: Testing the hypothesis on estimators or parameters?
So, what are you waiting for? Get started with the course so that you don’t make the same mistakes in your final exam!