A financial advisor wants to determine what factors influence a mutual funds rate of return. A random sample of 1-year return rates (expressed as a percentage) for 78 mutual funds was collected along with measures of the age of the fund (rounded to the nearest year), the risk profile of the fund (high or low risk), the amount invested in the fund (in millions of dollars), and the expense to manage the fund (expressed as a percentage). A portion of the data is given in Table 9.7.

Use the information from the printout in Figure 9.21 and answer each of the following questions \((\alpha=0.10)\) :

a. Which variables are continuous and which variables are discrete (nominal/ ordinal)?

b. Write the population regression equation.

c. Write the estimated regression equation.

d. Is the overall model useful in predicting the rate of return?

e. What are the effects of each of the different predictor (independent) variables? Interpret any and all significant effects.

f. Find and interpret the coefficient of determination.
g. Determine you believe that whether any of your predictor variables are highly correlated with each other.

h. Do you think the given model is a good model for predicting the rate of return? Justify your answer.

Figure 9.21

Table 9.7

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Method Categorical predictor coding (1,0) Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 4 1011.46 252.866 24.10 0.000 Age 1 0.40 0.396 0.04 0.847 Amount Invested 1 2.79 2.788 0.27 0.608 Expense 1 9.10 9.104 0.87 0.355 Risk Profile 1 982.14 982.140 93.60 0.000 Error 73 765.99 10.493 Total 77 1777.45 Model Summary S R-sq R-sq(adj) R-sq(pred) 56.91% 3.23929 54.54% 51.14% Term Coefficients Coef SE Coef T-Value P-Value VIF Constant 11.83 1.49 7.95 0.000 Age 0.0066 0.0340 0.19 0.847 1.02 Amount Invested -0.0082 0.0160 -0.52 0.608 1.02 Expense 0.568 0.609 0.93 0.355 1.04 Risk Profile Low -7.334 0.758 -9.67 0.000 1.06 Regression Equation Risk Profile High Return Rate = 11.83 +0.0066 Age - 0.0082 Amount Invested + 0.568 Expense Low Return Rate = 4.49 + 0.0066 Age - 0.0082 Amount Invested + 0.568 Expense Fits and Diagnostics for Unusual Observations Return Obs Rate Fit Resid 8 12.620 4.670 7.950 Std Resid 2.51 R 2.97 R 9 14.720 5.316 9.404 R Large residual