1. For the past decade, the regression equation for therelationship between rate

Question

1. For the past decade, the regression equation for therelationship between rate of return for the Dow Jones IndustrialAverage (X) and a particular Mutual Fund (Y) is
Ù
Y = 110 – 16 X

a. Assuming this relationship continues, if for a given yearthe Dow is up 8%, what would you predict the rate of return for theMutual Fund to be? (assume that the regression slope andintercept were derived from data in the percent format, notdecimals).

b. For every 1% increase in the Dow, what would you expect tohappen to the Mutual Fund?

c. If the rate of return for the Dow were 0 for a given year,what would you predict the return rate to be for the Mutual Fund inthat year?

d. If in a given year the Dow were up 10% and the Mutual Fundwere down 20%, using the above prediction equation, what is theresidual (error in prediction) for this year? Does thisresidual indicate an overestimate or an underestimate of the MutualFund performance?

Explanation / Answer

Given that

Ypredicted = 110-16X

Y: Mutual Fund return

X: Dow Jones return

a)      When X is up 8% then

Ypredicted = 110-16*8 = -18%         

b)      For every 1% increase in Dow Jonesthe Mutual fund should get y= -16*1 = -16% return.

c)       If return from Dow Jones =0% then we should predict 110-16* 0% =110% rate of return from themutual Fund

d)      If Dow Jones is up 10% thepredicted Y = 110-16*10 = -50%

And Y actual = -20%

Therefore residual error = Y actual – Y predicted =-20% - (-50%) = 30%

This is an underestimate of the rate of return.

Hope this helps. Feel free to ask for any clarifications

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