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HOMEWORK

QUESTIONS

Subject

Code

and

Title

STAT

2000:

Quantitative

Analysis

Assessment

Module

5:

Homework

questions

Additional

Information

When

there

is

evidence

of

academic

dishonesty,

a

student

will

face

Misconduct

Procedures.

Please

refer

to

Torrens

policies

and

procedures

in:

http://www.torrens.edu.au/about/policies

Instructions

Answer

these

questions

and

problems

Chapter

14

Questions

and

problems

23,

24,

25,

26,

27,

28,

29,

30,

33,

34,

40

Use

the

following

data

and

Microsoft

Excel

program

to

answer

questions

23?30.

The

table

gives

monthly

rates

of

return

for

3-??month

treasury

bills;

the

value

weighted

New

York

Stock

Exchange

Index;

and

Chrysler,

Ford,

and

GM

stock.

23.

In

finance,

we

are

often

interested

in

how

the

return

of

one

stock

is

related

to

some

market

index

such

as

the

NYSE.

The

model

we

usually

estimate

to

understand

this

relationship

is

known

as

the

market

model

and

is

given

by

the

equation

R

j,

t

=

?j

+

?

j

R

m,

t

+

e

j,

t

where:

R

j,

t

=

return

on

stock

j

in

month

t

R

m,

t

=

return

on

some

market

index

in

month

t

?j =

intercept

of

the

regression

line

?j

=

slope

of

the

regression

line

e

j,

t =

a

random

error

term

Use

Excel

to

do

the

following:

(a)

Draw

a

scatter

diagram

for

Ford

and

the

NYSE

index.

(b)

Estimate

the

parameters

?

and

?.

(c)

Compute

SSE,

SSR,

SST,

R2,

and

the

standard

error

of

the

estimate

for

this

regression.

(d)

Compute

the

standard

error

for

b,

and

use

a

t-??

test

to

test

the

significance

of

the

slope

of

the

regression.

Page

1

of

4

24.

In

finance,

we

sometimes

choose

to

estimate

the

capital

asset

pricing

(CAPM)

version

of

the

market

model,

which

is

given

by

the

equation

where

Rj,t

is

the

return

on

a

risk-??free

asset

(such

as

T-??bills)

in

month

t.

Repeat

parts

(a)?(d)

of

question

23

for

the

CAPM

version

of

the

market

model

using

the

Excel

program.

25.

Using

R2

as

the

measure

of

goodness

of

fit,

compare

the

market

model

estimated

in

question

23

with

the

CAPM

version

estimated

in

question

24.

26.

Find

a

95

%

confidence

interval

for

the

slope

coefficients

you

calculated

in

questions

23

and

24.

Which

estimate

of

?

has

the

wider

confidence

interval?

Page

2

of

4

27.

Suppose

we

are

interested

in

testing

whether

?

is

equal

to

1.

Then

we

would

test

H0:

?

=

1

against

H1:

?

?1.

Using

the

model

given

in

question

23,

test

this

hypothesis.

28.

Repeat

questions

23?27,

using

GM

stock?s

rates

of

return.

29.

Repeat

questions

23?27,

using

Chrysler

stock?s

rates

of

return.

30.

Suppose

we

are

interested

in

the

relationship

between

the

return

on

the

risk-??free

asset

(T-??bills)

and

the

return

on

the

NYSE

index.

(a)

Estimate

the

intercept

and

the

slope

for

a

regression

of

R

m,

t

on

R

f,

t.

(b)

Compute

the

standard

error

of

the

regression

and

use

a

t-??

test

to

test

the

significance

of

b.

(c)

Calculate

a

99

%

confidence

interval

for

b.

33.

When

estimating

the

relationship

between

the

price

of

a

good

and

the

quantity

of

the

good

sold

(the

demand

curve),

economists

sometimes

choose

to

transform

the

price

and

quantity

data

by

taking

the

natural

logarithm

of

both.

When

this

is

done,

the

slope

coefficient

b

can

be

interpreted

as

the

price

elasticity

of

demand

(the

sensitivity

of

quantity

to

changes

in

price).

Consider

the

following

information

on

the

price

and

quantity

of

So-??Good

Candy

Bars.

Price

($)

Quantity

1.50

100

1.25

135

1.00

175

0.75

225

0.50

300

0.25

500

Use

the

EXCEL

program

to

answer

the

following:

(a)

Estimate

the

elasticity

of

demand

for

these

data.

(b)

Use

a

t-??

test

to

test

the

significance

of

b.

(c)

Construct

a

95

%

confidence

interval

for

the

price

elasticity.

34.

The

batting

instructor

of

the

Minnesota

Twins

is

interested

in

the

relationship

between

number

of

hours

of

batting

practice

and

batting

average.

He

collects

the

following

data

on

8

players:

Hours

of

batting

practice

per

week

5

8

9

10

11

9

7

6

Batting

Average

0.265

0.277

0.254

0.320

0.301

0.260

0.230

0.272

Use

the

EXCEL

program

to

answer

the

following:

Page

3

of

4

(a)

Draw

a

scatter

diagram

for

these

data.

(b)

Compute

the

regression

parameters

a

and

b.

(c)

Compute

the

standard

error

of

b,

and

use

a

t

-??test

to

test

the

significance

of

the

slope

of

the

regression.

(d)

Construct

a

95

%

confidence

interval

for

b.

40.

Investment

advisors

sometimes

recommend

holding

gold

as

part

of

an

investor?s

portfolio,

because

the

value

of

gold

appears

to

be

negatively

related

to

that

of

the

stock

market.

Thus,

when

the

stock

market

goes

down

in

value,

the

value

of

gold

goes

up

in

value,

and

some

of

the

investor?s

losses

in

the

market

are

offset

by

gains

in

the

value

of

her

or

his

gold.

The

accompanying

table

shows

data

on

annual

rates

of

return

for

a

gold

mutual

fund

and

for

the

S&P

500.

Year

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

Gold

mutual

fund

151.30

70.70

-??18.90

47.30

8.20

-??25.30

-??11.00

30.10

51.50

11.30

S&P

500

18.16

31.48

-??4.85

20.37

22.30

5.97

31.05

18.75

5.24

16.58

Use

EXCEL

to

answer

the

following

questions:

(a) Estimate

the

slope

of

the

regression

of

the

rates

of

return

of

the

gold

mutual

fund

against

those

of

the

S&P

500.

(b)

Use

a

t-??

test

to

test

the

hypothesis

that

b

<

0.

(c)

If

you

expect

the

rate

of

return

to

be

20

%

next

year

(1989),

what

is

the

rate

of

return

of

the

gold

mutual

fund

you

expect?

Page

4

of

4

Paper#9210697 | Written in 27-Jul-2016

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