STAT 301 - Business Statistics
Lecture Review #26 - Introduction to Correlation and Regression

Review questions:

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

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

3) What does it mean 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:

1) Anastasia Romanova collects data on the number of customers per day at a small retail store, and the store’s daily sales volume. Data are below:

a) Compute the slope and intercept of the regression line. Interpret these quantities.

b) What is the correlation for these data?

2) 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 correlation coefficient for these data.

SOLUTIONS:
1a) slope = 20, intercept = 0
1b) correlation = 0.992
2a) 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.)
2b) correlation = .5