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    Regression and testing of hypothesis problems

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    Attached Data Files: FUNDS - This file contains 185 rows of data points
    1st Column : Fund Name
    2nd Column : Fund Type (Balanced = 1, Equity-Income = 2, Growth and Income = 3, Growth = 4, Aggressive-Growth = 5, Small-Company = 6, International and Global =7)
    3rd Column : Five Year investment performance
    4th Column : 1992 Return (in percentage)

    ? Calculate descriptive (or summary) statistics for the entire sample. What are the mean five year performance and mean 1992 return?
    Standard and Poor's 500 Stock Index (commonly called S & P 500) is the widest general-market index of stocks produced by the U.S. credit-rating agency Standard and Poor. The index is constituted by using the prices of securities of 425 U.S. industrial companies and 75 railway and public-utility corporations. Investors regard the S & P 500 as representing the market, the general level of the price of securities in the U.S. The success of an investment strategy is often measured by the degree to which the strategy beats the S & P 500. The reason for this is that by holding a portfolio that represents the S & P 500 (a Market Index Fund), one can do nearly as well as the S & P 500. The S & P 500 is often used as a base level for comparison. The five-year performance and 1992 return for the S & P 500 are $15,440 and 8%, respectively.
    1. Taking these as base level performance figures, what does that say about the investment abilities exhibited by the managed mutual funds in the study?
    2. Next, look at the five-year performance first. Construct side-by-side boxplots, forming groups based on the different types of funds. What can you say about risk based on the boxplots? Also, examine descriptive (or summary) statistics separated by type of mutual fund. Are there differences in five-year performance relating to fund type? Do certain types of funds seem to have been more successful than others over this time period? Are the patterns surprising, given that the market did well during this time period?
    3. Do you note any unusual funds in terms of performance from examination of the boxplots? Do you see any relationship between the variability of returns for a given fund type and the performance itself? Given the general investing axiom that higher performance goes with higher risk, what sort of relationship would you expect to exist?
    4. Now shorten the time horizon from five-year to one-year (1992) performance. Repeat the analyses previously done on the five-year return variable. Are there differences related to fund type? Are any observed differences between fund types similar to ones observed for five-year performance? What does that imply about the connection between short and long-term performance? Another way to investigate this is by constructing a scatter plot of one-year versus five-year performance. Does this plot suggest that funds that do well (or poorly) on one measure necessarily do well (or poorly) on the other?
    5. Based on your analysis from above, you identified that the 5 year performance and 1992 Return are different for the various funds.
    6. Conduct a "t" test using 5-step hypothesis testing procedure for the different funds (compare say "Balanced with respect to others). What do you conclude?
    7. Repeat the analysis using either Kruskal Wallis test or Wilcoxon Rank Sum test for the different funds. Is the conclusion the same as in the "t" test? Why?
    8. Construct a scatter plot of the 1992 Return (vertical axis) versus the Five Year Return (horizontal axis). Does it appear that a linear regression model would be appropriate for these data?
    9. Now, calculate/plot the least squares regression line for predicting the 1992 return from the five year return. Is there a significant relationship between the two variables? Prove or disprove it with an appropriate test. Do you notice any apparent systematic violations of the regression assumptions?
    10. Construct and examine the regression diagnostics for this model.
    (a) Do you notice any outlier? If yes, remove the outlier and rerun the regression.
    (b) Is the regression model satisfactory?
    (c) Do you notice any apparent systematic violations of the regression assumptions?

    What will you advise an investor like me to do, given that I have access to these mutual funds?

    Please show detailed steps towards solution.

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    Solution Preview

    Please see the attached files.

    Descriptive Statistics

    Case Summaries

    Fund Type Five Year Performance 1992 Return (%)
    Balanced N 25 25
    Mean 14068.92 7.44
    Std. Deviation 815.814 3.675
    Minimum 12548 1
    Maximum 15628 15
    Range 3080 14
    Median 14222.00 8.00
    Skewness .171 .105
    Variance 665551.743 13.507
    Equity Income N 17 17
    Mean 14160.24 9.41
    Std. Deviation 1185.966 3.483
    Minimum 12219 1
    Maximum 16423 15
    Range 4204 14
    Median 14259.00 9.00
    Skewness .125 -.543
    Variance 1406514.691 12.132
    Growth & Income N 32 32
    Mean 14642.41 8.63
    Std. Deviation 1711.071 4.463
    Minimum 12714 0
    Maximum 22331 19
    Range 9617 19
    Median 14301.00 7.50
    Skewness 3.081 .167
    Variance 2927764.701 19.919
    Growth N 25 25
    Mean 15536.24 10.52
    Std. Deviation 2150.302 6.312
    Minimum 12784 0
    Maximum 22934 25
    Range 10150 25
    Median 15593.00 9.00
    Skewness 1.696 .511
    Variance 4623800.357 39.843
    Aggressive Growth N 20 20
    Mean 17331.10 8.15
    Std. Deviation 2917.345 8.713
    Minimum 12433 -9
    Maximum 24161 28
    Range 11728 37
    Median 17674.00 9.50
    Skewness .455 .264
    Variance 8510903.358 75.924
    Small Company N 37 37
    Mean 17219.84 10.92
    Std. Deviation 1973.854 9.145
    Minimum 14348 -3
    Maximum 21995 41
    Range 7647 44
    Median 17182.00 12.00
    Skewness .764 .739
    Variance 3896099.751 83.632
    International & Global N 29 29
    Mean 11381.14 -3.17
    Std. Deviation 1256.596 5.029
    Minimum 9426 -14
    Maximum 13726 4
    Range 4300 18
    Median 11337.00 -3.00
    Skewness .383 -.095
    Variance 1579033.623 25.291
    All funds combined N 185 185
    Mean 14936.32 7.35
    Std. Deviation 2659.452 7.845
    Minimum 9426 -14
    Maximum 24161 41
    Range 14735 55
    Median 14570.00 8.00
    Skewness .674 .227
    Variance 7072686.371 61.544

    Ans. 1.

    Five Year Performance 1992 Return (%)
    Mean 14936.32 7.35
    Base level value 15440 8.00

    From the table above we can see that the investment abilities exhibited by managed funds are below the base level performance

    From the box plot we can see that different funds perform differently. International and Global fund have performed poor. There are some funds which have a very good performance there list in the box plot as outliers

    Descriptive Statistics

    Fund Type Five Year Performance
    Balanced 14068.92
    Equity Income 14160.24
    Growth & Income 14642.41
    Growth 15536.24
    Aggressive Growth 17331.10
    Small Company 17219.84
    International & ...

    Solution Summary

    The solution gives details of students t test and regression analysis problems with interpretations of the results obtained. Null Hypothesis, alternative hypothesis, critical value, p value, decision rule, confidence level, test statistic, slope, intercept, correlation, residual, r square, coefficient of determination, regression coefficients, independent variable, dependent variable, least square estimation and scatter diagram are given.