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A portion of a data set containing information for 45 mutual funds that are part of the Morningstar Funds 500 follows. The complete data set is available in the file named MutualFunds. The data set includes the following five variables: Fund Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income). Net Asset Value ($): The closing price per share on December 31, 2007. 5-Year Average Return (%): The average annual return for the fund over the past five years. Expense Ratio (%): The percentage of assets deducted each fiscal year for fund expenses. Morningstar Rank: The risk adjusted star rating for each fund; Morningstar ranks go from a low of 1-Star to a high of 5-Stars. Fund Name Fund Type Net Asset Value ($) 5-Year Average Return (%) Expense Ratio (%) Morningstar Rank Amer Cent Inc &amp; Growth Inv DE 28.88 12.39 .67 2-Star American Century Intl. Disc IE 14.37 30.53 1.41 3-Star American Century Tax-Free Bond FI 10.73 3.34 .49 4-Star American Century Ultra DE 24.94 10.88 .99 3-Star Ariel DE 46.39 11.32 1.03 2-Star Artisan Intl Val IE 25.52 24.95 1.23 3-Star Artisan Small Cap DE 16.92 15.67 1.18 3-Star Baron Asset DE 50.67 16.77 1.31 5-Star Brandywine DE 36.58 18.14 1.08 4-Star . . . . . . . . . . . . . . . . . . a. Develop an estimated regression equation that can be used to predict the 5-year average return given the type of fund. At the .05 level of significance, test for a significant relationship. b. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain. c. Develop the estimated regression equation that can be used to predict the 5-year average return given the type of fund, the net asset value, and the expense ratio. At the .05 level of significance, test for a significant relationship. Do you think any variables should be deleted from the estimated regression equation? Explain. d. Morningstar Rank is a categorical variable. Because the data set contains only funds with four ranks (2-Star through 5-Star), use the following dummy variables: 3Star-Rank = 1 for a 3-Star fund, 0 otherwise; 4StarRank = 1 for a 4-Star fund, 0 otherwise; and 5StarRank = 1 for a 5-Star fund, 0 otherwise. Develop an estimated regression equation that can be used to predict the 5-year average return given the type of fund, the expense ratio, and the Morningstar Rank. Using a = .05, remove any independent variables that are not significant. e. Use the estimated regression equation developed in part (d) to predict the 5-year average return for a domestic equity fund with an expense ratio of 1.05% and a 3-Star Morningstar Rank.

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Statistics for Business & Economic...

12th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9781285846323

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Section
BuyFindarrow_forward

Statistics for Business & Economic...

12th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9781285846323
Chapter 15, Problem 56SE
Textbook Problem
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A portion of a data set containing information for 45 mutual funds that are part of the Morningstar Funds 500 follows. The complete data set is available in the file named MutualFunds. The data set includes the following five variables:Fund Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income).Net Asset Value ($): The closing price per share on December 31, 2007.5-Year Average Return (%): The average annual return for the fund over the past five years. Expense Ratio (%): The percentage of assets deducted each fiscal year for fund expenses. Morningstar Rank: The risk adjusted star rating for each fund; Morningstar ranks go from a low of 1-Star to a high of 5-Stars. Fund Name Fund Type Net Asset Value ($) 5-Year Average Return (%) Expense Ratio (%) Morningstar Rank Amer Cent Inc & Growth Inv DE 28.88 12.39 .67 2-Star American Century Intl. Disc IE 14.37 30.53 1.41 3-Star American Century Tax-Free Bond FI 10.73 3.34 .49 4-Star American Century Ultra DE 24.94 10.88 .99 3-Star Ariel DE 46.39 11.32 1.03 2-Star Artisan Intl Val IE 25.52 24.95 1.23 3-Star Artisan Small Cap DE 16.92 15.67 1.18 3-Star Baron Asset DE 50.67 16.77 1.31 5-Star Brandywine DE 36.58 18.14 1.08 4-Star . . . . . . . . . . . . . . . . . . a. Develop an estimated regression equation that can be used to predict the 5-year average return given the type of fund. At the .05 level of significance, test for a significant relationship. b. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain. c. Develop the estimated regression equation that can be used to predict the 5-year average return given the type of fund, the net asset value, and the expense ratio. At the .05 level of significance, test for a significant relationship. Do you think any variables should be deleted from the estimated regression equation? Explain. d. Morningstar Rank is a categorical variable. Because the data set contains only funds with four ranks (2-Star through 5-Star), use the following dummy variables: 3Star-Rank = 1 for a 3-Star fund, 0 otherwise; 4StarRank = 1 for a 4-Star fund, 0 otherwise; and 5StarRank = 1 for a 5-Star fund, 0 otherwise. Develop an estimated regression equation that can be used to predict the 5-year average return given the type of fund, the expense ratio, and the Morningstar Rank. Using a = .05, remove any independent variables that are not significant. e. Use the estimated regression equation developed in part (d) to predict the 5-year average return for a domestic equity fund with an expense ratio of 1.05% and a 3-Star Morningstar Rank.

a.

To determine

Find an estimated regression equation that could be used to predict the 5-year average return given the type of fund.

Perform a test to check the significant relationship between variables at α=0.05 level of significance.

Explanation of Solution

Calculation:

The data related to the type of fund, net asset value, 5 year average return, expense ratio and management risk of 45 mutual funds.

Multiple linear regression model:

A multiple linear regression model is given as E(y)=β0+β1x1+...+βpxp where E(y) is the expected value of response or dependent variable, and x1,x2,...,xp are the k quantitative independent variables with categorical variables having 0 or 1. The quantities β1,β2,...,βp are the estimated slopes corresponding to x1,x2,...,xp respectively and β0 are the estimated intercept of the line, from the sample data.

The dummy variable FundDE is defined as is,

FundDE={1for a domestic equality fund0    otherwise

The dummy variable FundIE is defined as is,

FundIE={1for an international fund0    otherwise

Indicator variable:

Software procedure:

Step by step procedure to create indicator variable using MINITAB software is given as,

• Choose Calc>Make Indicator variables.
• InMake indicator variables for, enterFund Type.
• In Distinct Value, enter 1 for DE and0 for IE, FI.
• Click OK.

The indicator variable is stored in the column of ‘FundDE’.

Software procedure:

Step by step procedure to create indicator variable using MINITAB software is given as,

• Choose Calc>Make Indicator variables.
• InMake indicator variables for, enterDrive.
• In Distinct Value, enter 1 for IE and0 for DE, FI.
• Click OK.

The indicator variable is stored in the column of ‘FundIE’.

In the given problem, five year average return be the dependent variable (y), FundDE be the independent variable (x1) and FundIE be the independent variable (x2)

b.

To determine

Whether the estimated regression equation in part (a) provides a good fit.

c.

To determine

Find an estimated regression equation that could be used to predict the 5-year average return given the type of fund, the net asset value and the expense ratio.

Perform a test to check the significant relationship between variables at α=0.05 level of significance.

Explain whether any variable should be deleted from the estimated regression equation.

d.

To determine

Find an estimated regression equation that could be used to predict the 5-year average return given the type of fund, the expense ratio and the Morningstar Rank.

Perform a test at α=0.05 level of significance and remove an independent variable that is not significant.

e.

To determine

Predict the 5-year average return for a domestic equality fund with an expense ratio of 1.05% and a 3-star Morningstar Rank.

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