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Interpreting Scatter Diagram, and Independent/Dependent Variable

Mutual Fund Data

Sample Number Assets ($ millions) Return (%)
1 AARP 622.2 10.8
2 Babson 160.4 11.3
3 Compass 275.7 11.4
4 Galaxy 433.2 9.1
5 Keystone 437.9 9.2
6 MFS Bond A 494.5 11.6
7 Nichols 158.3 9.5
8 T Rowe 681 8.2
9 Thompson 241.3 6.8

Construct a scatter diagram with the correct dependent and independent variables. I have to choose the "causing" variable for X, and the variable being "caused" or influenced for Y, and understand it enough to discuss it.

I am struggling with computing the coefficients of correlation, and determining and discussing what they mean.

The most difficult is testing the significance of the sample correlation to be computed above.

Finally, I am then to develop a regression equation and predict a return for $400M in assets. I have to explain if the equation I used is meaningful or not, and explain why or why not.

During this whole process, I am to highlight every statistic needed to address the problem and discuss what each means, showing all 5 steps necessary to test the significance of the correlation. The five steps are to state the hypothesis, state the test statistic, state the decision rule (e.g. if Ho = zero, we must fail to reject the null), calculate the test statistic, and interpret the results and state the conclusion.

Please provide details step-by step, or a real-world and extremely simplified explanation of how to arrive at the solution.

Solution Preview

Please see the attached files.

Answer
Data:
Y (Return %) X( Assets)
10.80 622.20
11.30 160.40
11.40 275.70
9.10 433.20
9.20 437.90
11.60 494.50
9.50 158.30
8.20 681.00
6.80 241.30

In the present problem, the given data relates total asset holdings of various mutual fund companies and the corresponding percentage returns. It is natural to assume that return of various companies should depend on the total value of their asset holdings. Hence, in this problem the "causing" variable X (or independent variable) is assets and the variable being "caused" Y (dependent variable) are returns.
Scatter Diagram

Results of the regression analysis
SUMMARY OUTPUT

Regression ...

Solution Summary

The solution assists in interpreting scatter diagram and independent/dependent variable.

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