STAT 440 - Forecasting
Lecture Review #2 - Review of Correlation and Regression

Recall that following each class there will be a lecture review assignment. These assignments are designed to keep you current on course material, to reinforce learning by repetition of key ideas and computations, and to structure your investigation of class materials beyond the in-class lectures and activities. Lecture review assignments are due at the beginning of the following class period. They may be typed or neatly hand-written. Multi-page submissions will of course be stapled. PLEASE label your paper with your name and the assignment number (to facilitate giving you proper credit). You should SHOW YOUR WORK on computational problems.

Review questions:

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

2) What is the correlation? What does it measure?

3) What is meant, by a correlation of +1? Of -1? Of 0?

4) What is the coefficient of determination (commonly called r-square)? How is it interpreted?

5) How are the slope and intercept of a (simple linear) regression model obtained? How are they interpreted?

Computational exercises:

1) 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) Sketch an appropriate graph of the data. Does a linear fit appear reasonable?

b) Find (by hand) the correlation coefficient for these data. Interpret this number.

c) Find (by hand) the slope and intercept of the regression line for these data. Interpret these numbers.

2) The dataset "DJI-SP.xlsx", from this website, contains daily values of the Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P), for a ten year period (2014-2024). Download that data file, and use it for the following.

a) Find the correlation between DJIA and S&P, for this ten-year period. Construct a graph which illustrates the relationship.

b) For each day, compute the percent return on each index. For example: If the index goes from 1000 to 1100, the return is (1100-1000)/1000=0.10, or ten percent. (NOTE that we will not be able to compute the return for the last day in the data set.)

c) Find the mean and the standard deviation of the DJIA daily returns. Of the S&P daily returns.

d) Find the correlation between DJIA and S&P daily returns, for this ten-year period. Construct a graph which illustrates the relationship.

e) Compute the slope and intercept for a regression model that predicts daily percentage change in the S&P 500, given daily percentage change in the DJIA. Interpret these numbers.

SOLUTIONS:
1b) r = .5
1c) slope = .1, intercept = .5. NOTE: the intercept should correspond with the risk-free rate (short term Treasury bill)
2b) corr = 0.8
2c) slope = 20, intercept = 0