LINEAR REGRESSION – AN 80-YEAR STUDY OF

THE DOW JONES INDUSTRIAL AVERAGE

Courtney Verdree

AP Statistics

Introduction

. The purpose of this project was to determine whether or not the Dow Jones Averages would be a good investment and to graph the data for interpretation.

Linear Graph

Exponential Graph

Power Graph

1. Describe the association between “DJIA price” and “Years Since 1930”.

The association between the price and the years since is a positive linear correlation.

2. What is the equation for your linear model? (Use descriptive variables)

Dow Price = 125.3(years)-2.4425x10^05

3. Interpret the slope of the line in context. The slope of my line is  125.3x the year. The

slope is fairly steep.

4. Does the y-intercept of your model have a meaningful interpretation or is it just a hypothetical base value? Explain.

Yes, because the y-intercept tells us what y is when X equals 0.

5. Look at the residuals plot for your linear model. Do you have any concerns about predictions made by your model? Explain. No because the graphs look similar, the

only difference is the directions change , one is positive and one is negative.

6. What is the equation of your new model? (Use descriptive variables) Y hat= .06234(year)-166

7. Interpret the slope of the line in context. The slope is .06234 , which describes the

movement in the line for every x and y value.

8. This time, does the y-intercept of your model have a meaningful interpretation? Explain Yes because it has positive strong

correlation between the data and the R2 is close to 100%.

9. The residuals plot for your transformed model still doesn’t look perfect, but has it improved? How do you feel about the appropriateness of your new model? Yes the residual plots has improved because its

showing a much stronger correlation. It is appropriate for my new model.

10. What is the correlation for your transformed data? What does this indicate about the association? The correlation .9357. this indicates that it’s a linear positive relationship and that the exponential graph would be the best fit to interpret the data.

11. What is R2 for your transformed data? Interpret this value in context. R2 for my transformed data is 0.94 and it

explains that 94% of the variation in y is determined by the variation in x. This shows a positive association.

12. Use your model to make a prediction about the Dow price in July of 2012. y hat= .06234(2012)-116

= 9.42808

13. You will most likely retire some time between 2040 and 2050. What does your model predict for the Dow price in 2045? Comment on the appropriateness of this prediction. =.06234(2045)-116

=11.4853

e^11.4853= 972425.26

14. What is the equation of the exponential model that Microsoft Excel fit to the original data? Y hat=.06234(year)-116

15. Use the exponential model to make a prediction about the Dow price in 2012. Compare it to the prediction made by your model. Are they close? Y hat=.06234(2012)-116

=9.42808

e^9.42808=12432.63

16. Calculate the y-intercept of your model and the y-intercept of the exponential model. Are they close? Are these predictions lower or higher than the actual Dow price on that date? Original model is -2.44e, the y-intercept

for the exponential model -116. The predictions for the exponential model is lower than the original model.

17. Recently, concerns about the U.S. economy, unemployment rate, national debt, foreign relations, the world economy, financial troubles in countries like Greece and China, climate change, and population expansion, among others have led many to question whether common stocks will continue to grow at 10-12% as we move into the future. Soon, you will have finished college, secured a position in a fulfilling career, and started earning a rewarding salary. You, too, will have to make decisions about the best way to invest your hard earned money in order to insure that you have a healthy nest egg to retire on. You’ve just studied the trend of the broader market over an 80-year period that included numerous wars, periods of political unrest, economic recessions, energy crises, population shifts, and corporate scandals (just to name a few). So, are you convinced? How do you feel about the strength of this trend? Will the market continue to reward you the way it rewarded long-term investors of the previous century? Or, will these new troubling developments send you seeking other methods of investment? Explain.

yes, I am not convinced , America has a very strong economy and In another 80 years the government will see many more changes, but they can fix it. Yes I would invest into the company because the exponential graph fits better on the line of best fit and its better for your money to grow exponentially then linearly.