Quant 2.1

Question 1

What is Multiple Regression? How do you model it? What should be your focus in the process?

Answer 1

• Multiple linear regression is used to understand correlations and make predictions by running a linear relationship model between one dependent variable and two or more independent variables.
• It requires some statistical software to run the regression (a complex process)
• We should be focused to choose and specify the model without any errors and an analyst should understand and be able to interpret what is the output of the software in which we ran the regression.

Question 2

Why do we use multiple regression models in the investment world?

Answer 2

• To forecast
• To identify relationships or correlations between variables
• *To test existing theories
• Model is nothing but an equation which the statistical software will come up with!

Question 3

What is the regression model?

Answer 3

• Yi = bzero + b1x1 + b2x2 + error term

Here, Yi is the dependent variable, bzero is the intercept coefficient and x1 & x2 are the independent variables.

Question 4

What is the intercept coefficient? (bzero)

Answer 4

• The intercept coefficient represents the expected value of Yi (dependent variable) if all independent variables are zero.

Question 5

What are k slope coefficients?

Answer 5

• K is the number of independent variables in a regression model. They’re called as slope coefficients or regression coefficients which measure how much the dependent variable changes when the independent variable changes by one unit holding all other independent variables constant.

Question 6

What are the assumptions underlying the multiple regression?

Answer 6

• Linearity: The relationship between the dependent and the independent variables is linear.
• Homoskedasticity: The variance of regression residuals is the same (in the same range) for all observations. (regression residuals are the predicted values of Y by the model vs the actual value of Y which has been calculated) variance is the average of the squared differences from the mean.
• Independence of errors: The residuals of regression are also called as the errors. This assumption, implies that the residuals are uncorrelated across observations.
• Normality: The residuals are assumed to be normally distributed.
• Independence of the independent variables: First, the independent variables shouldn’t be random. Next, there should be no linear relation between two or more of the independent variables or the combinations of the independent variables.

Question 7

How to check if the assumptions are being violated or not?

Answer 7

• The software produces some diagnostic plots which can help detect if these assumptions are violated.

Question 8

Which scatter plot is used to diagnose which type of assumption violation?

Answer 8

• For linearity, Y and any of the independent variable is checked to see if they show a linear relationship.
• Then the predicted values of residuals versus actual residuals found in the regression are compared for heteroskedasticity (the variance should lie within a same range)
• The the errors are compared with independent variables to check if the residuals are independent from the independent variables or not. (there shouldn’t be any correlation which can be observed in the residuals and the independent variables, if observerd then the residuals in the regression are misspecified.)
• Q-Q plot to check if the residuals are normally distributed or not
• The scatter plots of independent variables are compared to some other independent variable to determine if there is a linear relationship that exists among the independent variables or not.