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Memorial University of NewfoundlandEconomicsECON 4550

Roberto Martinez-Esineira!ssi"nment 4

Name___________________________________

Computer problem:

Use the GRETL dataset "beer" and regress the quantity of beer on its price.

1. Report the results in table and equation format [3]2. Comment on the results obtained [5]

3. Predict the residuals and plot them against the price of beer [3]

4. Fomally test and comment on the significance of the slope parameter [5]

5. Using still the dataset "beer" regress the quantity of beer on "other liquor" price.

6. Report the results in table and equation format [3]

7. Comment on the results obtained [5]

8. Predict the residuals and plot them against the price of other liquor [3]

9.

Fomally test and comment on the significance of the slope parameter [5]

10. Plot the price of beer against the price of other liqours and provide a measure of the correlation

between the two variables [3]

11. Explain whether the signs you saw are the expected ones and why or why not. Explain

whether you would be able to think about a better way to find out how the price of beer and

other liquors affects the quantity demanded of beer [5]

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

[3 each

]An estimator is

1)

_______A)

a random variable.

B)

an estimate.

C)

a formula that gives an efficient guess of the true population value.

D)

a nonrandom number.

2

An estimate is

2)

_______

A)

another word for estimator.

B)

a nonrandom number.

C)

unbiased if its expected value equals the population value.

D)efficient if it has the smallest variance possible.

3The critical value of a two-sidedt-test computed from a large sample

3)

_______

A)

is 1.96 if the significance level of the test is 5%.

B)

is 1.64 if the significance level of the test is 5%.

C)

cannot be calculated unless you know the degrees of freedom.

D)

is the same as thep-value.

4The correlation coefficient

4)

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_______

A)

is close to one ifXcausesY.

B)

lies between zero and one.

C)

takes on a high value if you have a strong nonlinear relationship.

D)is a measure of linear association.

5Degrees of freedom

5)

_______

A

ensure that = .

B)

are (n-2) when replacing the population mean by the sample mean.

C)

in the context of the sample variance formula means that estimating the mean uses up some of the information in the

datA

D)

is something that certain undergraduate majors at your university/college other than economics seem to have an

amount of.

6

When the estimated slope coefficient in the simple regression model,1, is zero, then

6)

_______

A)

0

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7)

_______

A)

ESS>TSS

B)

ESS=SSR+TSS

C)

TSS=ESS+SSR

D)

R2=1 - (ESS/TSS)

8Binary variables

8)

_______

A)

can take on more than two values.

B)

can take on only two values.

C)

are generally used to control for outliers in your sample.

D)

exclude certain individuals from your sample.

9The following are all least squares assumptions with the exception of:

9)

_______

A) The conditional distribution ofuigivenXihas a mean of zero.

B)

(Xi,Yi),i=1,...,nare independently and identically distributed draws from their joint distribution.

C)

The explanatory variable in regression model is normally distributed.

D)

Large outliers are unlikely.

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The slope estimator,1, has a smaller standard error, other things equal, if

10)

______

A)

there is more variation in the explanatory variable,X.

B)

there is a large variance of the error term,u.

C)

the intercept,0, is small.

D)

the sample size is smaller.

The regressionR2is a measure of

11)

______

A)

whether or notXcausesY.

B)

the square of the determinant ofR.

C)

whether or notESS>TSS.

D)

the goodness of fit of your regression line.

To obtain the slope estimator using the least squares principle, you divide the

12)

______

A)

sample covariance ofXandYby the sample variance ofY.

B)

sample variance ofXby the sample variance ofY.

C)

sample variance ofXby the sample covariance ofXandY.

D)

sample covariance ofXandYby the sample variance ofX.

13) Which of the following

13) Which of the following is not an assumption of the multiple regression model?

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A)

The

values

of each

x

not

rando

m and

are not

exactlinearfunctio

ns of

the

other

explan

atory

variabl

es.

)

var!y

"var!e

"

#)

The

leasts$ua

res

estimato

rs

are%&

'.()

cov!y

y

cov!e

e

!i*)

1+

)

,n

themulti

ple

reg

res

sio

n

model which of the following does -T lead to larger variances of the least s$uares estimators b/and

var!b/)?

A) larger error variances0 s/

) larger correlation between x/and x3#) smaller values of !x i/ x/)

/

() larger correlation between x/and y

12) ow can you estimate nonlinear function forms using least s$uares?

A) estimate the linear approximation over small ranges at a time

) transform0 such as s$uaring or cubing0 some explanatory variables.

#) use a very large sample so you do not have to assume the error terms are normally distributed

() ,t cannot be done. 4ou need to use another estimation techni$ue.

15) When performing an 6test0 if the null hypothesis is H0: b2= b3= 0 what is the alternative

hypothesis?

A) b/7 and b37

) b/7 or b37

#) !b/7 and b3"7) or !b/"7 and b37)

() !b/87 and b397) or !b/97 and b387)

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1:

)

o

w

do

esom

itti

ng a relevant variable from a regression model affect the estimated coefficient of other variables in the

model?

A) they are biased downward and have smaller standard errors

) they are biased upward and have larger standard errors

#) they are biased and the bias can be negative or positive

() they are unbiased but have larger standard errors

1;) ,f you re*ect the null hypothesis when performing a ero

) the original model is incorrectly specified and can be improved upon

#) relevant variable are omitted and the coefficient estimates of included variables are biased() an incorrect functional form was used

1) The following @incer e$uation has been used to estimate wages

ln !Y) " ln !Yo) B b2EDUB b3EXPERB b4EXPER/B e

where Yis income0 Y7is income of someone with no education or experience0EDUis years of education

andEXPERis experience in the field. ,f you suspect males earn higher wages than females and that the

wage difference increases with education how would you ad*ust the econometric model to estimate wages?

A) include a binary variable for gender0MALE) include an interaction term e$ual toMALE* EDU#) include an indicator variable forMALEand one forFEMALE() include a binary variable forMALEand an interaction term e$ual to MALE * EDU

/7) The #how test is a specific application of a!n)

A) >test) c/test

#) 6test

() ttest