Statistics - Correlation coefficient
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We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its five-year performance. The question is: Can the five-year rate of return be estimated based on the assets of the fund? Nine mutual funds were selected at random, and their assets and rates of return are shown below.
Fund Assets ($ millions) Return (%) Fund Assets ($ millions) Return (%)
AARP High Quality Bond $622.2 10.8 MFS Bond A$494.5 11.6
Babson Bond L 160.4 11.3 Nichols Income 158.3 9.5
Compass Capital Fixed Income 275.7 11.4 T. Rowe Price Short-term 681.0 8.2
Galaxy Bond Retail 433.2 9.1 Thompson Income B 241.3 6.8
Keystone Custodian B-1 437.9 9.2
1. Draw a scatter diagram.
2. Compute the coefficient of correlation.
3. Compute the coefficient of determination.
4. Write a brief report of your findings for parts b and c.
5. Determine the regression equation. Use assets as the independent variable.
6. For a fund with $400.0 million in sales, determine the five-year rate of return (in percent)
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Solution Summary
This solution addresses 6 statistics questions that include drawing a scattergram, determining coefficients of both correlation and determination and the regression equation.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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