Deck 2: Sample Exam for Chapters 4-5

Question 1

One of the shortest but most important sections in the book is that on the Gauss-Markov theorem.
(a) What is the Gauss-Markov theorem?
(b) Carefully explain what the precise properties specified by the Gauss-Markov theorem mean and why they are desireable for an equation.
(c) What could cause the Gauss-Markov theorem to no longer hold? What should we do in such a situation?

Answer 1

See Section 4.3.

Question 2

In Chapter 4, we discussed seven explicit assumptions about the properties of a regression equation. These assumptions (or, more accurately, the first six of them) are usually referred to as the Classical Assumptions.
(a) Carefully and accurately state the seven assumptions.
(b) State what each assumption actually means in real-world terms (be extremely brief).

Answer 2

See Section 4.1.

Question 3

Briefly identify the following in words or equations as appropriate:
(a) p-value
(b) Sampling distribution of
$\hat { \beta }$ (c) Type I Error
(d) Level of significance
(e) Given $\hat { \beta }$ = 4.0 and SE ( $\hat { \beta }$ ) = 2.0, test the null hypothesis that $\beta$ = 0 (versus the alternative hypothesis that it does not equal zero) with 13 degrees of freedom at the 1% level of significance.

Answer 3

(a) See page 135.
(b) See Section 4.2.
(c) See Section 5.1.
(d) See Section 5.2.
(e) t = 2.0, and the critical two-sided, 1%, 13 degree of freedom critical t-value is 3.012, so we can not reject the null hypothesis.

Question 4

Consider the following regression equation for the United States (standard errors in parentheses):
$$\begin{array} { c } \hat { \mathrm { P } } _ { \mathrm { t } } = 4.00 - 0.010 \mathrm { PRP } _ { \mathrm { t } } + 0.030 \mathrm { PRB } _ { \mathrm { t } } + 0.20 \mathrm { YD } _ { \mathrm { t } } \\( 0.005 ) \quad ( 0.020 ) \quad ( 0.04 ) \\\overline { \mathrm { R } } ^ { 2 } = 0.98 \quad \mathrm { n } = 29\end{array}$$ where: P_t =per capita pounds of pork consumed in time period t
PRP_t =the price of pork in time period t
PRB_t =the price of beef in time period t
YD_t =per capita disposable income in time period t
(a) Hypothesize signs and specify the appropriate null and alternative hypotheses for the coefficients of each of these variables.
(b) State your decision rules and then test your hypotheses on the above results using the t-test at a 5% level of significance.
(c) If you could add one variable to the regression, what variable would you add? Why?