DS280 - Intro to Statistics

Lecture Review #22 - Regression

REVIEW QUESTIONS:

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

2) What is the correlation? How is it computed?

3) What is meant if the correlation is positive? Negative? Zero? What is the largest (smallest) value a correlation can have?

4) What are the slope and intercept of a regression line? How are they 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 correlation coefficient for these data. Interpret this number.

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

SOLUTIONS:

a) r = .5. There is a moderately strong relationship between return and risk; as risk increases, return tends to do so as well.

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

      intercept = .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.)