DS350 - Quantitative Methods

Lecture Review #17 - Regression

Review questions:

1) What is the covariance? What does it measure? How is it computed?

2) What are the slope and intercept of a regression line? How are they computed?

3) What is the error variance of a regression model? How is it computed?

Computational exercises:

The security market line describes the relationship between the return on a security and its risk (as measured by its beta coefficient). Remember that "return is a function of risk" - so a stock's return is our "Y" variable and its risk is our "X" variable in this context. Data for five stocks are given below.

a) Find the slope and intercept of the regression line for these data. Interpret these numbers.

b) Find the error variance for the regression line.

SOLUTIONS:

a) slope = 0.1. On average, increasing your risk (beta) by 1 will increase your return by .1% monthly.

    intercept = 0.5. When your risk (beta) is 0, your return will by .5% monthly, on average. (This should correspond with the "risk-free rate" - that is, what you would get from a 90-day Treasury bill.)

b) s_e² = 0.004