linear regression an 80 year study of the dow jones industrial average

Linear Regression- An 80 Year study of the Dow

Jones Industrial AverageTehya Singleton

Rivers AP Statistics

Chart Copied From Fathom

Year Since 1930 Dow Price Predicted Dow Price Residuals Transformation Dow Price Transformation Prediction Transformation Residuals ln since 1930 ln dow price1930 0 233.99 -2435.42 -2669.41 2.3692 1.87328 0.495915 #Domain error# 5.455281931 1 135.39 -2310.12 -2445.51 2.13159 1.90036 0.231231 0 4.908161932 2 53.89 -2184.83 -2238.72 1.73151 1.92743 -0.195921 0.693147 3.986941933 3 90.77 -2059.54 -2150.31 1.95794 1.9545 0.00343931 1.09861 4.508331934 4 88.05 -1934.24 -2022.29 1.94473 1.98158 -0.0368473 1.38629 4.47791935 5 126.23 -1808.95 -1935.18 2.10116 2.00865 0.0925124 1.60944 4.838111936 6 164.86 -1683.65 -1848.51 2.21712 2.03572 0.181392 1.79176 5.10511937 7 184.01 -1558.36 -1742.37 2.26484 2.0628 0.202044 1.94591 5.214991938 8 141.2 -1433.06 -1574.26 2.14983 2.08987 0.0599637 2.07944 4.950181939 9 143.26 -1307.77 -1451.03 2.15612 2.11694 0.0391804 2.19722 4.964661940 10 126.14 -1182.47 -1308.61 2.10085 2.14402 -0.0431653 2.30259 4.837391941 11 128.79 -1057.18 -1185.97 2.10988 2.17109 -0.0612096 2.3979 4.858181942 12 105.72 -931.884 -1037.6 2.02416 2.19817 -0.174008 2.48491 4.660791943 13 137.25 -806.59 -943.84 2.13751 2.22524 -0.0877265 2.56495 4.92181944 14 146.11 -681.295 -827.405 2.16468 2.25231 -0.0876325 2.63906 4.984361945 15 162.88 -556.001 -718.881 2.21187 2.27939 -0.0675183 2.70805 5.093011946 16 201.56 -430.706 -632.266 2.3044 2.30646 -0.00205528 2.77259 5.306091947 17 183.18 -305.412 -488.592 2.26288 2.33353 -0.0706552 2.83321 5.210471948 18 181.33 -180.117 -361.447 2.25847 2.36061 -0.102137 2.89037 5.200321949 19 175.92 -54.8228 -230.743 2.24532 2.38768 -0.142365 2.94444 5.170031950 20 209.4 70.4717 -138.928 2.32098 2.41475 -0.0937773 2.99573 5.344251951 21 257.86 195.766 -62.0938 2.41138 2.44183 -0.0304436 3.04452 5.552421952 22 279.56 321.061 41.5008 2.44648 2.4689 -0.0224261 3.09104 5.633221953 23 275.38 446.355 170.975 2.43993 2.49597 -0.0560423 3.13549 5.618151954 24 347.92 571.65 223.73 2.54148 2.52305 0.0184311 3.17805 5.851971955 25 465.85 696.944 231.094 2.66825 2.55012 0.118124 3.21888 6.143861956 26 517.81 822.239 304.429 2.71417 2.5772 0.136975 3.2581 6.249611957 27 508.52 947.533 439.013 2.70631 2.60427 0.102039 3.29584 6.23151958 28 502.99 1072.83 569.838 2.70156 2.63134 0.0702167 3.3322 6.220571959 29 674.88 1198.12 523.242 2.82923 2.65842 0.17081 3.3673 6.514531960 30 616.73 1323.42 706.687 2.7901 2.68549 0.104605 3.4012 6.424431961 31 705.37 1448.71 743.341 2.84842 2.71256 0.135854 3.43399 6.558721962 32 597.93 1574.01 976.076 2.77665 2.73964 0.0370134 3.46574 6.393471963 33 695.43 1699.3 1003.87 2.84225 2.76671 0.0755429 3.49651 6.54453

1964 34 841.1 1824.6 983.495 2.92485 2.79378 0.131063 3.52636 6.734711965 35 881.74 1949.89 1068.15 2.94534 2.82086 0.124483 3.55535 6.78191966 36 847.38 2075.18 1227.8 2.92808 2.84793 0.0801469 3.58352 6.742151967 37 904.24 2200.48 1296.24 2.95628 2.875 0.0812788 3.61092 6.807091968 38 883 2325.77 1442.77 2.94596 2.90208 0.0438822 3.63759 6.783331969 39 815.47 2451.07 1635.6 2.91141 2.92915 -0.0177441 3.66356 6.703761970 40 734.12 2576.36 1842.24 2.86577 2.95623 -0.0904586 3.68888 6.598671971 41 858.43 2701.66 1843.23 2.9337 2.9833 -0.0495944 3.71357 6.755111972 42 924.74 2826.95 1902.21 2.96602 3.01037 -0.0443532 3.73767 6.829511973 43 926.4 2952.25 2025.85 2.9668 3.03745 -0.0706479 3.7612 6.831311974 44 757.43 3077.54 2320.11 2.87934 3.06452 -0.185177 3.78419 6.629931975 45 831.51 3202.83 2371.32 2.91987 3.09159 -0.171726 3.80666 6.723241976 46 984.64 3328.13 2343.49 2.99328 3.11867 -0.12539 3.82864 6.892281977 47 890.07 3453.42 2563.35 2.94942 3.14574 -0.196317 3.85015 6.79131978 48 862.27 3578.72 2716.45 2.93564 3.17281 -0.237171 3.8712 6.759571979 49 846.42 3704.01 2857.59 2.92759 3.19989 -0.272302 3.89182 6.741021980 50 935.32 3829.31 2893.99 2.97096 3.22696 -0.256001 3.91202 6.840891981 51 952.34 3954.6 3002.26 2.97879 3.25404 -0.275243 3.93183 6.858921982 52 808.6 4079.9 3271.3 2.90773 3.28111 -0.373375 3.95124 6.69531983 53 1199.22 4205.19 3005.97 3.0789 3.30818 -0.229283 3.97029 7.089431984 54 1115.28 4330.49 3215.21 3.04738 3.33526 -0.287872 3.98898 7.016861985 55 1347.45 4455.78 3108.33 3.12951 3.36233 -0.232817 4.00733 7.205971986 56 1775.31 4581.07 2805.76 3.24927 3.3894 -0.140129 4.02535 7.481731987 57 2572.07 4706.37 2134.3 3.41028 3.41648 -0.00619381 4.04305 7.852471988 58 2128.73 4831.66 2702.93 3.32812 3.44355 -0.11543 4.06044 7.663281989 59 2660.66 4956.96 2296.3 3.42499 3.47062 -0.0456344 4.07754 7.886331990 60 2905.2 5082.25 2177.05 3.46318 3.4977 -0.0345213 4.09434 7.974261991 61 3024.82 5207.55 2182.73 3.4807 3.52477 -0.0440714 4.11087 8.014611992 62 3393.78 5332.84 1939.06 3.53068 3.55184 -0.0211608 4.12713 8.12971993 63 3539.47 5458.14 1918.67 3.54894 3.57892 -0.0299799 4.14313 8.171731994 64 3764.5 5583.43 1818.93 3.57571 3.60599 -0.0302844 4.15888 8.233371995 65 4708.47 5708.73 1000.26 3.67288 3.63307 0.0398145 4.17439 8.457121996 66 5528.91 5834.02 305.11 3.74264 3.66014 0.0825007 4.18965 8.617751997 67 8222.61 5959.31 -2263.3 3.91501 3.68721 0.227797 4.20469 9.01464

1998 68 8883.29 6084.61 -2798.68 3.94857 3.71429 0.234288 4.21951 9.091931999 69 10655.1 6209.9 -4445.25 4.02756 3.74136 0.2862 4.23411 9.27382000 70 10522 6335.2 -4186.78 4.0221 3.76843 0.253664 4.2485 9.261222001 71 10522.8 6460.49 -4062.32 4.02213 3.79551 0.226625 4.26268 9.26132002 72 8736.59 6585.79 -2150.8 3.94134 3.82258 0.118762 4.27667 9.075282003 73 9233.8 6711.08 -2522.72 3.96538 3.84965 0.115727 4.29046 9.130632004 74 10139.7 6836.38 -3303.33 4.00603 3.87673 0.129298 4.30407 9.224212005 75 10640.9 6961.67 -3679.24 4.02698 3.9038 0.123178 4.31749 9.272462006 76 11185.7 7086.97 -4098.71 4.04866 3.93087 0.117788 4.33073 9.322392007 77 13212 7212.26 -5999.73 4.12097 3.95795 0.16302 4.34381 9.488882008 78 11378 7337.55 -4040.47 4.05607 3.98502 0.0710448 4.35671 9.339442009 79 9171.61 7462.85 -1708.76 3.96245 4.0121 -0.0496499 4.36945 9.123872010 80 10465.9 7588.14 -2877.8 4.01978 4.03917 -0.0193908 4.38203 9.25588

Graphs and Questions

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

There is a strong positive linear relationship between the two variables

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Collection 1 Scatter Plot

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Dow _Price = 125Since_1930 - 2.4e+03; r2 = 0.63


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

Dow price=125.3(since 1930)-2.4425

3. Interpret the slope of the line in context. As the “years since” increases the “Dow Price” also

increases.

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

The y-intercept is the Dow price over 80 years. It is a meaningful interpretation these are numbers from the stock market there is always a meaning behind those numbers.

5. Look at the residuals plot for your linear model. Do you have any concerns about predictions made by your model? Explain.

No, the residual plot looks exactly like the linear model the only difference is the direction they are facing.

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Transformation_Dow _Price = 0.0271Since_1930 + 1.87; r2 = 0.94


6. What is the equation of your new model? (Use descriptive variables)

Transformation Dow price=0.02707(since 1930)-50.38

7. Interpret the slope of the line in context. • As the “years since” increases the “Dow Price” also

increases.

8. This time, does the y-intercept of your model have a meaningful interpretation? Explain.

• Yes it’s the same data it’s just a transformation of the data

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Transformation_Dow _Price = 0.0271Since_1930 + 1.87; r2 = 0.94

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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?

• It has improved. Its looks like the linear model so it’s appropriate to use.

Collection 1

Transformation_Dow_Price

Year 0.972085

S1 = correlation

10. What is the correlation for your transformed data? What does this indicate about the association?

The correlation is 0.97 there is a strong positive association

11. What is R2 for your transformed data? Interpret this value in context. R2 is 0.94 and that tells us that 94% of the variation in y is explained by the variation in x 12. Use your model to make a prediction about the Dow price in July of 2012. The predicted Dow price for July 2012 is 252101.1575

13. You will most likely retire sometime between 2040 and 2050. What does your model predict for the Dow price in 2045? Comment on the appropriateness of this prediction.

• The predicted Dow price for 2045 is 256236.0575 that prediction is fairly appropriate based on the fact that as the years go by the predicted Dow price increases.

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ln_dow _price = 0.0623Since_1930 + 4.3; r2 = 0.94


14. What is the equation of the exponential model that Microsoft Excel fit to the original data?

ln Dow price= 0.0623(x)+4.3

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?

The prediction made by the exponential model is 129.6476. No they are not close.

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?

• Y intercept for linear model (-244250)• Y intercept for exponential model (116)• They are not close• These predictions are lower than the actual Dow price

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.

I am convinced. Even with the new troubling developments I feel that there will still be a strong trend in the future because this isn’t the first time that there has been problems facing the economy. The market is never down for to long and I am confident that it will continue to reward myself and future investors like it has for the previous.

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ln_dow _price = 1.41ln_since_1930 + 2; r2 = 0.73

Collection 1 Scatter Plot0

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Linear

Exponential

Power

The exponential graph best fits the data gathered in this study.

linear regression an 80 year study of the dow jones industrial average

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