Question 6.78
43. Fidelity Investments, like other large mutual fund companies, offers many “sector funds” that concentrate their investments in narrow segments of the stock market. These funds often rise or fall by much more than the market as a whole. Here are the percent returns for 23 Fidelity “Select Portfolios” funds for the years 2002 (when stocks fell) and 2003 (when stocks went up).
| 2002 return | 2003 return | 2002 return | 2003 return | 2002 return | 2003 return |
|---|---|---|---|---|---|
| −17.1 | 23.9 | −0.7 | 36.9 | −37.8 | 59.4 |
| −6.7 | 14.1 | −5.6 | 27.5 | −11.5 | 22.9 |
| −21.1 | 41.8 | −26.9 | 26.1 | −0.7 | 36.9 |
| −12.8 | 43.9 | −42.0 | 62.7 | 64.3 | 32.1 |
| −18.9 | 31.1 | −47.8 | 68.1 | −9.6 | 28.7 |
| −7.7 | 32.3 | −50.5 | 71.9 | −11.7 | 29.5 |
| −17.2 | 36.5 | −49.5 | 57.0 | −2.3 | 19.1 |
| −11.4 | 30.6 | −23.4 | 35.0 |
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Do a careful statistical analysis of these data, using both graphs and whatever numerical measures you think are appropriate. Make a side-by-side comparison of the distributions of returns in 2002 and 2003 and also describe the relationship between the returns of the same funds in these two years. What are your most important findings? (The outlier is Fidelity Gold Fund.)
43.
Answers will vary. Below are plots that would be useful for the analyses.
One-variable analysis:
If the outlier for the 2002 returns is removed, the mean and standard deviation become −19.68 and 16.06, respectively.
Two-variable analysis:
The equation of the least-squares regression line is predicted . After removing the outlier, the equation becomes predicted . This regression line appears to do a better job of summarizing the pattern in the data.