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1. What is the relationship, if any, between t -distributed and F -distributed random variables?(a) A t -variate with z  degrees of freedom is also an F (1, z )(b) The suare of a t -variate with z  degrees of freedom is also an F (1, z )(!) A t -variate with z  degrees of freedom is also an F ( z , 1)(d) There is no relationship between the two distributions.

". #onsider a simple regression model with !oe$!ient standard errors !al!ulated using the

usual formulae. Whi!h of the following statements is%are !orre!t regarding the standard error

estimator for the slope !oe$!ient?

(i) &t varies positively with the suare root of the suares of residual (s)(ii) &t varies positively with the spread of X  about its mean value(iii) &t varies positively with the spread of X  about 'ero(iv) &t varies positively with the sample si'e T 

(a) (i) only(b) (i) and (iv) only(!) (i), (ii) and (iv) only(d) (i), (ii), (iii) and (iv).

 . What result is proved by the auss-*ar+ov theorem?

(a) That gives unbiased !oe$!ient estimates

(b) That gives minimum varian!e !oe$!ient estimates

(!) That gives minimum varian!e !oe$!ient estimates only among the !lass of linear

unbiased estimators

(d) That ensures that the errors are distributed normally

/. Whi!h of the following is 0T !orre!t with regard to the p-value atta!hed to a test statisti!?

(a) p-values !an only be used for two-sided tests

(b) &t is the marginal signi!an!e level where we would be indi2erent between re3e!ting and

not re3e!ting the null hypothesis

(!) &t is the e4a!t signi!an!e level for the test

(d) iven the p-value, we !an ma+e inferen!es without referring to statisti!al tables

5. What is the relationship, if any, between the normal and t -distributions?(a) A t -distribution with 'ero degrees of freedom is a normal(b) A t -distribution with one degree of freedom is a normal(!) A t -distribution with innite degrees of freedom is a normal(d) There is no relationship between the two distributions.

6. Two resear!hers have identi!al models, data, !oe$!ients and standard error estimates. They test the same hypothesis using a two-sided alternative, but resear!her 1 uses a 57 si'eof test while resear!her " uses a 187 test. Whi!h one of the following statements is !orre!t?

(a) 9esear!her " will use a larger !riti!al value from the t -tables(b) 9esear!her " will have a higher probability of type & error(!) 9esear!her 1 will be more li+ely to re3e!t the null hypothesis(d) :oth resear!hers will always rea!h the same !on!lusion.

;. Whi!h of the following !onditions must be fullled for the <urbin Watson test to be valid?

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(i) The regression in!ludes a !onstant term(ii) The regressors are non-sto!hasti!(iii) There are no lags of the dependent variable in the regression(iv) There are no lags of the independent variables in the regression

(a) (i), (ii) and (iii) only(b) (i) and (ii) only(!) (i), (ii), (iii) and (iv)(d) (i), (ii), and (iv) only

=. &f the residuals of a regression on a large sample are found to be heteros!edasti! whi!h of 

the following might be a li+ely !onseuen!e?

(i) The !oe$!ient estimates are biased(ii) The standard error estimates for the slope !oe$!ients may be too small(iii) tatisti!al inferen!es may be wrong

(a) (i) only(b) (ii) and (iii) only(!) (i), (ii) and (iii)(d) (i) and (ii) only

>. &n the estimated model ?log( ) 2.25 0.7log( ) 0.02i i i

q p y= − +  where p is the pri!e and q is the

demanded uantity of a !ertain good and y  is disposable in!ome, what is the meaning of the!oe$!ient on log (p)?

(a) &f the pri!e in!reases by 17, the demanded uantity will be 8.88;7 lower on average,!eteris paribus(b) &f the pri!e in!reases by 17, the demanded uantity will be ;87 lower on average,!eteris paribus(!) &f the pri!e in!reases by 17, the demanded uantity will be 8.;7 lower on average,

(d) 0one of the answers above is !orre!t

 To answer uestions 18 through 1" !onsider the following estimated model (by ), where

return is the total return of holding a rm sto!+ during one year, dkr is the rm@s debt to

!apital ratio, eps denotes earnings per share, netinc denotes net in!ome and salary  denotes

total !ompensation, in millions of dollars, for the # (estimated standard errors of the

parameters in parentheses below the estimates).

 The model was estimated using data on nB 1/" rms.

?

2

12.3 0.32 0.043 0.005 0.0035

. (6.89) (0.15) (0.078) (0.0047) (0.0022)

0.07644 0.03468 0.58234 0.28928 0.11393

142 0.0395

i i i ireturn dkr eps netinc salary

 s e

 p val 

n R

= − + + − +

−

= =

18. What !an you say about the estimated !oe$!ient of the variable salary ? (!onsider a one-

sided alternative for testing signi!an!e of the parameters and use the 0ormal appro4imation)

(a) Cor ea!h additional million dollars in the wage of the #, return is predi!ted to

in!rease by 8.885, on average, ceteris paribus. :ut it is not statisti!ally signi!ant at a

57 level of signi!an!e.

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(b) Cor ea!h additional million dollars in the wage of the #,  return is predi!ted to

de!rease by 8.885, on average, ceteris paribus. And it is statisti!ally signi!ant at a57

level of signi!an!e.

(!) Cor ea!h additional million dollars in the wage of the #, return is predi!ted to

in!rease by 8.85, on average, ceteris paribus. And it is statisti!ally signi!ant at a

17level of signi!an!e.

(d) &t is statisti!ally signi!ant at a 57level of signi!an!e but it is not signi!ant at 17level of signi!an!e.

11. The model is estimated without in!luding the variables dkr  and eps, and an 9"B8.8=; was

obtained. What is the value of the C-statisti! for testing the null hypothesis that the

!oe$!ients on dkr  and eps are both 'ero?

(a) ".="1(b) 8.85;8(!) 8.8=8=(d) We have not enough information to answer this uestion, we would need to gathermore information from the restri!ted model.

1". What !an you say about the !oe$!ient on dkr  (!onsider a one-sided alternative for testing

signi!an!e of the parameters and use the 0ormal appro4imation)

(a) &t is statisti!ally signi!ant at a 57 level of signi!an!e and also signi!ant at 17levelof signi!an!e(b) &t is statisti!ally signi!ant at 17 level of signi!an!e(!) &t is statisti!ally signi!ant at a 17 level of signi!an!e but it is not signi!ant at 57level of signi!an!e(d) &t is statisti!ally signi!ant at a 57 level of signi!an!e but it is not signi!ant at 17level of signi!an!e(e) 0one of the answers above is !orre!t

1. &n testing multiple e4!lusion restri!tions in the multiple regression model under the#lassi!al assumptions, we are more li+ely to re3e!t the null that some !oe$!ients are 'ero ifD(a) The 9esiduals sum of suares of the restri!ted model is large relative to that of theunrestri!ted model(b) The 9esiduals sum of suares of the restri!ted model is small relative to that of theunrestri!ted model(!) The total sum of suares,T, is large(d) The inter!ept parameter is greater than the signi!an!e level(e) :oth a) and d) above(f) :oth !) and d) above

1/. Testing for the normality of residual, statisti! #hi-suare(") B 1.8 with p-value B

8.88888, the !on!lusion should beD

a. error is normally distributedb. error isn@t normally distributed!. 0o !on!lusion yet

1 2 3 4 5 6 7 8 9 10 11 12 13 14

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B A C A C B A B C A B D A B

Q10 and 12: remember for one-sided t-test p-a!"e # "s"a! p-a!"e$2