Linear Regression – An 80-Year Study
of the Dow Jones Industrial Average
For decades, the prevailing opinion in the field of finance has been that, given a long
investment horizon (30 years or more), the best results will be achieved through
investment in the common stock of publicly sold corporations. It is often cited that the
long-term average annualized return of the broader stock market is between 10% and
12%. That percentage has changed slightly over time depending on who is citing it and
when it is being cited. However, if you had purchased a diversified basket of stocks of
domestic corporations at any point during the middle of the 20th century and held them
for 30 years, you would have achieved an average annualized return somewhere in this
range.
The index that is commonly used to indicate the health of the broader stock market is the
Dow Jones Industrial Average (DJIA). The Dow is made up of 30 large-cap (blue chip)
companies. The DJIA is calculated by summing the stock prices of these 30 companies
and then adjusting that sum for stock splits or other structural changes to the companies’
shares. The result is a dollar value that generally fluctuates in unison with the broader
market. We use the DJIA to give us a sense of how the overall stock market is faring at
any given point in time.
Your goal in this project is to study the trend in the DJIA since 1930 and create an
appropriate model. You will be using Microsoft Excel to create a spreadsheet and
appropriate displays of the data.
1. Collect data on the DJIA—Research the Dow price for the month of July (any
date near the beginning of the month is fine) in each year from 1930 to 2010.
Enter them into an Excel Spreadsheet with a column for the years and a
column for the Dow prices. Scale the years appropriately.
2. Create an appropriate display to show the trend in the DJIA over the past 80
years. Answer question #1.
3. Create a linear model to predict “DJIA price” from “Years Since 1930”.
Include the model in your display. Answer questions #2, 3, and 4.
4. Create a column for predicted Dow Prices and fill it with the predicted price
for each year based on your model. Create a column for residuals and fill it
with the residual for each year. Create a residuals plot. Answer question #5.
5. Perform transformations on the Dow Prices until you find an appropriate one
that makes the plot look more linear. Create a column in your spreadsheet for
these transformed values, give it an appropriate heading, and fill it with the
transformed price for each year. Create a new display of your transformed
data.
6. Create a linear model for the transformed data and include the model in your
display. Answer questions #6, 7, and 8.
7. Create a column for predictions made by your new model, give it an
appropriate heading, and fill it with the appropriate predicted values. Create a
column for residuals and fill it with the residuals for each year. Create a
residuals plot. Answer question #9.
8. Calculate the correlation coefficient, r, and the R2 value for your transformed
data. Answer questions #10 and 11.
9. Answer questions #12 and 13.
10. Use Microsoft Excel to fit an exponential curve to the original data (Dow
prices vs. Years Since 1930). Answer questions #14, 15, and 16.
11. Answer question #17.
The top row of your spreadsheet should look like this:
Predicted
Since
Dow
Year 1930 Dow Price Price
Residuals
(Appropriate
Transformation (Predictions
(Residuals
Which You
Based on Your
From Your
Have Chosen) Transformation) Transformation)