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A portion of a data set containing information for 45 mutual funds that are part of theMorningstar Funds 500 for 2008 follows. The complete data set is available in the filenamed Mutualfunds. The data set includes the following five variables:$\begin{array}{l}{\text { Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI }} \\ {\text { (Fixed Income). }}\end{array}$Net Asset Value (S): 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 gofrom a low of 1 -Star to a high of 5-Stars.$\begin{array}{l}{\text { a. Develop anestimated regression that can be used to predict the five-year average }} \\ {\text { retum given fund type. At the } .05 \text { level of significance, tes for a significant relationship. }} \\ {\text { b. Did the estimated regression equation developed in provide a good fit to the }} \\ {\text { data? Explain. }}\end{array}$$\begin{array}{l}{\text { c. Develop the estimated regression equation that can be use dict the five-year }} \\ {\text { average return given the type of fund, the net asset value, and the expense ratio. At the }} \\ {.05 \text { level of significance, test a significant relationship. Do you think any variables }} \\ {\text { should be deleted from the estimated regression equation? Explain. }}\end{array}$d. Morningstar Rank is a categorical variable. Because the data set contains only fundswith four ranks $(2-$ Star through 5 -Star), use the following dummy variables: 3 Star-Rank $=1$ for a 3 -Star fund, 0 otherwise; 4 StarRank $=1$ for a 4 -Star fund, 0 other-wise; and 5 StarRank $=1$ for a 5 -Star fund, 0 otherwise. Develop an estimatedregression equation that can be used to predict the five-year average return given thetype of fund, the expense ratio, and the Morningstar Rank. Using $\alpha=.05,$ remove anyindependent variables that are not significant.$\begin{array}{l}{\text { e. Use the estimated regression equation developed in part (d) to predict the five-year }} \\ {\text { average return for a domestic equity fund with an expense ratio of } 1.05 \% \text { and a } 3 \text { -Star }} \\ {\text { Momingstar Rank. }}\end{array}$

a) $\hat{y}=4.9090+10.4658 \mathrm{Fund} \mathrm{DE}+21.6823$ Fund IEb) good fitc) since Net Asset value is not significance and hence can be deleted.d) $\hat{y}=-4.6074+8.1713$ Fund $\mathrm{DE}+19.5194$ Fund IE $+5.5197$ Expense ratios $(\%)+5.92373$ StarRank$+8.23474$ StarRank $+6.62415$ StarRanke) 15.2833$\%$

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Cairn University

University of St. Thomas

Idaho State University

Boston College

Lectures

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02:16

Information about mutual f…

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Mutual funds are classifie…

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Morning star tracks the to…

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Statistics for investing $…

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04:37

01:42

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Top stock fund. The averag…

heart. A of this problem is asking to find the probability of a domestic equity funds. Do this. You do the number of domestic equity funds divided by the total number of mutual funds. This is 16 divided by 25 which equals a probability of 250.64 heart. Be asked, what is the probability of a fund with a four or five star rating? To do this, you take the number of funds with a four or five star rating and divided by the total number of mutual funds. The problem says that 13 mutual fund were rated three stars or less. So to find the number of mutual funds that were 45 stars, you have to do 25 minus 13. You then divide this by the total number of funds and get the probability of a fund with a four or five star rating, which is point for eight. Part C of this problem asks what is the probability of a fund that is both domestic equity in 45 stars? The problem says that seven domestic equity funds were four stars and to domestic equity funds were fast ours. You therefore, add these together to get the number of domestic equity funds that were four or five stars and divided by the total number of funds. So that is a seven plus two or nine divided by 25 which equals 250.36 Party. Asked what the probability of a fund that is domestic equity or four or five stars? The probability of on those domestic, domestic or four or five stars equals the probability of a being domestic equity, plus the probability of being +45 stars, minus the probability that is domestic and +45 stars. These values were calculated in the previous parts, so it's 0.64 the probability of a being domestic plus 0.48 the probability of it being four or five stars minus 0.36 The probability of being domestic and 45 stars, making the probability of a fund being domestic equity or four or five stars, equaling 50.76

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