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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

**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 *k* quantitative independent variables with categorical variables having 0 or 1. The quantities

The dummy variable FundDE is defined as is,

The dummy variable FundIE is defined as is,

*Indicator variable*:

**Software procedure:**

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

- Choose
**Calc>Make Indicator variables**. - In
**Make indicator variables for**, enter**Fund Type**. - In
**Distinct Value**, enter**1**for**DE**and**0**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**. - In
**Make indicator variables for**, enter**Drive**. - In
**Distinct Value**, enter**1**for**IE**and**0**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 (

**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

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

**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.

Statistics for Business & Economics, Revised (MindTap Course List)

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