A portion of the data set containing information for $45$ mutual funds that are part of the$$Morningstar Funds $500$for some year is provided. The data set includes the following five variables:

Fund Type: Domestic Equity $($DE$),$ International Equity $($IE$),$ Fixed Income $($FI$)$

Net Asset Value $($$$)$: The closing price per share on Dec $.31$

$5-$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.

Fund Rank: The risk adjusted rating for each fund. Lower is better. This column is not necessarily numerical $($hint$).$

Develop a regression model that can be used to predict the $5-$year average return using all of the other variables: fund type, the net asset value, the expense ratio, and the morning star rank.

What changes would you make to this model and why?

Develop a new model based on the recommendations in part $2.$

Use the model you developed in part $3$ to predict the $5-$year average return for a fund with the following characteristics. Ignore variables that are not in the model you developed in part $3.$

Fund type: DENet asset value: $27\mathrm{.}66$Expense ratio: $1\mathrm{.}05\%$Fund Rank: $2$ d Name

Fund

Type

Net Asset

Value $($$$)$

$5$ Year

Average

Return

$(\%)$

Expense

Ratio

$(\%)$

Fund

Ranking

Amer Cent Inc & Growth Inv DE $28\mathrm{.}8812\mathrm{.}540\mathrm{.}634$

American Century Intl. Disc IE $14\mathrm{.}3730\mathrm{.}681\mathrm{.}373$

American Century Tax$-$Free Bond FI $10\mathrm{.}733\mathrm{.}490\mathrm{.}452$

American Century Ultra DE $24\mathrm{.}9411\mathrm{.}030\mathrm{.}953$

Ariel DE $46\mathrm{.}3911\mathrm{.}470\mathrm{.}994$

Artisan Intl Val IE $25\mathrm{.}5225\mathrm{.}101\mathrm{.}193$

Artisan Small Cap DE $16\mathrm{.}9215\mathrm{.}821\mathrm{.}143$

Baron Asset DE $50\mathrm{.}6716\mathrm{.}921\mathrm{.}271$

Brandywine DE $36\mathrm{.}5818\mathrm{.}291\mathrm{.}042$

Brown Cap Small DE $35\mathrm{.}7316\mathrm{.}001\mathrm{.}162$

Buffalo Mid Cap DE $15\mathrm{.}2917\mathrm{.}40\mathrm{.}983$

Delafield DE $24\mathrm{.}3217\mathrm{.}921\mathrm{.}282$

DFA U$.$S$.$ Micro Cap DE $13\mathrm{.}4717\mathrm{.}380\mathrm{.}493$

Dodge & Cox Income FI $12\mathrm{.}514\mathrm{.}460\mathrm{.}402$

Fairholme DE $31\mathrm{.}8618\mathrm{.}380\mathrm{.}961$

Fidelity Contrafund DE $73\mathrm{.}1118\mathrm{.}140\mathrm{.}851$

Fidelity Municipal Income FI $12\mathrm{.}584\mathrm{.}560\mathrm{.}411$

Fidelity Overseas IE $48\mathrm{.}3923\mathrm{.}610\mathrm{.}862$

Fidelity Sel Electronics DE $45\mathrm{.}6013\mathrm{.}650\mathrm{.}853$

Fidelity Sh$-$Term Bond FI $8\mathrm{.}602\mathrm{.}910\mathrm{.}413$

Fideliy DE $39\mathrm{.}8514\mathrm{.}550\mathrm{.}522$

FPA New Income FI $10\mathrm{.}954\mathrm{.}780\mathrm{.}583$

Gabelli Asset AAA DE $49\mathrm{.}8116\mathrm{.}851\mathrm{.}322$

Greenspring DE $23\mathrm{.}5912\mathrm{.}611\mathrm{.}033$

Janus DE $32\mathrm{.}2612\mathrm{.}960\mathrm{.}863$

Janus Worldwide IE $54\mathrm{.}8312\mathrm{.}460\mathrm{.}824$

Kalmar Gr Val Sm Cp DE $15\mathrm{.}3015\mathrm{.}461\mathrm{.}283$

Managers Freemont Bond FI $10\mathrm{.}565\mathrm{.}290\mathrm{.}561$

Marsico $21$st Century DE $17\mathrm{.}4415\mathrm{.}311\mathrm{.}271$

Mathews Pacific Tiger IE $27\mathrm{.}8632\mathrm{.}851\mathrm{.}123$

Meridan Value DE $31\mathrm{.}9215\mathrm{.}481\mathrm{.}042$

Oakmark I DE $40\mathrm{.}379\mathrm{.}661\mathrm{.}014$

PIMCO Emerg Mkts Bd D FI $10\mathrm{.}6813\mathrm{.}721\mathrm{.}213$

RS Value A DE $26\mathrm{.}2723\mathrm{.}831\mathrm{.}322$

T$.$ Rowe Price Latin Am$.$ IE $53\mathrm{.}8951\mathrm{.}251\mathrm{.}202$

T$.$ Rowe Price Mid Val DE $22\mathrm{.}4617\mathrm{.}060\mathrm{.}762$

Templeton Growth A IE $24\mathrm{.}0716\mathrm{.}060\mathrm{.}973$

Thornburg Value A DE $37\mathrm{.}5315\mathrm{.}611\mathrm{.}232$

USAA Income FI $12\mathrm{.}104\mathrm{.}460\mathrm{.}583$

Vanguard Equity$-$Inc DE $24\mathrm{.}4213\mathrm{.}560\mathrm{.}252$

Vanguard Global Equity IE $23\mathrm{.}7121\mathrm{.}920\mathrm{.}601$

Vanguard GNMA FI $10\mathrm{.}374\mathrm{.}400\mathrm{.}171$

Vanguard Sht$-$Tm TE FI $15\mathrm{.}682\mathrm{.}520\mathrm{.}123$

Vanguard Sm Cp Idx DE $32\mathrm{.}5817\mathrm{.}160\mathrm{.}193$

Wasatch Sm Cp Growth DE $35\mathrm{.}4114\mathrm{.}131\mathrm{.}152$