Question 1

In the linear model $Y = a + b X + c Z$ , a test of the hypothesis that parameter c equals zero is

Accepted Answer

A)   an F-test.
B)   an R2-test.
C)   a zero-statistic.
D)   a t-test.
E)   a Z-test.  D

Question 2

The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
 $\begin{array}{rllll}
\text { DEPENDENT VARIABLE: } & \text { Y } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ON F } \
\text { OBSERVATIONS: } &18 & 0.3066 & 7.076 & 0.0171
\end{array}$

$\begin{array}{lllll}
\text { VARIABLE } & \begin{array}{llll}
\text { PARAMETER } \
\text { ESTIMATE }
\end{array} & \begin{array}{l}
\text { STANDARD } \
\text { ERROR }
\end{array} & \text { T-RATIO } & \text { P-VALUE } \
\text { INTERCEPT } & 15.48 & 5.09 & 3.04 & 0.0008\X&-21.36&8.03&-2.66&0.0171
\end{array}$
-The exact level of significance of $\hat { b }$ is

Accepted Answer

A)   0.171 percent.
B)   1 percent.
C)   1.71 percent.
D)   2.66 percent.
E)   2.921 percent.  C

Question 3

The sample regression line

Accepted Answer

A)   shows the actual (or true)  relation between the dependent and independent variables.
B)   is used to estimate the population regression line.
C)   connects the data points in a sample.
D)   is estimated by the population regression line.
E)   maximizes the sum of the squared differences between the data points in a sample and the sample regression line. B

Question 4

In the nonlinear function $Y = a X ^ { b } Z ^ { 2 }$ , the parameter c measures

Accepted Answer

A)   If  Δ\DeltaΔ Y / Δ\DeltaΔ Z.
B)   the percent change in Y for a 1 percent change in Z.
C)   the elasticity of Y with respect to Z.
D)   both a and c
E)   both b and c

Question 5

Refer to the following computer output from estimating the parameters of the nonlinear model
 $$\begin{array} { r l l l l l } 
\text { DEPENDENT VARIAELE: } & \text { LNY } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \
\text { OESERVATIONS: } & \text { 32 } & \mathbf { 0 . 7 7 5 6 } & \mathbf { 3 2 . 4 4 } & \mathbf { 0 . 0 0 0 1 } & \\
&  \text { PARAMETER } & \text { STANDARD } & & \
\text { VARIAELE }  & \text { ESTMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \

\text { INTEREEPT } & \mathbf { - 0 . 5 9 3 1 } & \mathbf { 0 . 3 2 } & \mathbf { - 2 . 1 7 } & \mathbf { 0 . 0 3 9 0 } \
\text { LNRR } & \mathbf { 4 . 6 5 } & 1.36 & \mathbf { 3 . 4 3 } & \mathbf { 0 . 0 0 1 9 } \
\text { LNS } & \mathbf { - 0 . 4 4 } & \mathbf { 0 . 2 4 } & - 1.83 & \mathbf { 0 . 0 7 7 4 } \
\text { LNT } & \mathbf { 8 . 2 8 } & \mathbf { 4 . 6 } & \mathbf { 1 . 8 0 } & \mathbf { 0 . 0 8 2 6 }
\end{array}$$
-The estimated value of a is

Accepted Answer

A)   -0.6931
B)   0.50
C)   -3.67
D)   2.66

Question 6

To test whether the overall regression equation is statistically significant one uses

Accepted Answer

A)   the t-statistic.
B)   the R2-statistic.
C)   the F-statistic.
D)   the standard error statistic.

Question 7

Refer to the following computer output from estimating the parameters of the nonlinear model
 $$\begin{array} { r l l l l l } 
\text { DEPENDENT VARIAELE: } & \text { LNY } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \
\text { OESERVATIONS: } & \text { 32 } & \mathbf { 0 . 7 7 5 6 } & \mathbf { 3 2 . 4 4 } & \mathbf { 0 . 0 0 0 1 } & \\
&  \text { PARAMETER } & \text { STANDARD } & & \
\text { VARIAELE }  & \text { ESTMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \

\text { INTEREEPT } & \mathbf { - 0 . 5 9 3 1 } & \mathbf { 0 . 3 2 } & \mathbf { - 2 . 1 7 } & \mathbf { 0 . 0 3 9 0 } \
\text { LNRR } & \mathbf { 4 . 6 5 } & 1.36 & \mathbf { 3 . 4 3 } & \mathbf { 0 . 0 0 1 9 } \
\text { LNS } & \mathbf { - 0 . 4 4 } & \mathbf { 0 . 2 4 } & - 1.83 & \mathbf { 0 . 0 7 7 4 } \
\text { LNT } & \mathbf { 8 . 2 8 } & \mathbf { 4 . 6 } & \mathbf { 1 . 8 0 } & \mathbf { 0 . 0 8 2 6 }
\end{array}$$
-Which of the parameter estimates are statistically significant at the 90% level of confidence?

Accepted Answer

A)   All the parameter estimates are statistically significant.
B)   All parameter estimates except  a^\hat { a }a^  and b^\hat { b }b^  are statistically significant.
C)    a^\hat { a }a^  is not statistically significant, but all the rest of the parameter estimates are significant.
D)    c^\hat { c }c^  is not statistically significant, but all the rest of the parameter estimates are significant.

Question 8

Refer to the following nonlinear model which relates W to P, Q, and R:
 $W = a P ^ { b } Q ^ { c } R ^ { d }$ 
The computer output form the regression analysis is:
 $$\begin{array} { r l l l l l } 
\text { DEPENDENTVARIAELE: } & \text { LNW } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \
\text { OESERVATIONS: } & \text { 19 } & \mathbf { 0 . 9 0 2 3 } & 43.12 & \mathbf { 0 . 0 0 0 1 } & \\
&  \text { PARAMETER } & \text { STANDARD } & & \
\text { VARIAELE }  & \text { ESTMMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \
\text { INTERCEPT } & \mathbf { 2 . 5 0 } & \mathbf { 0 . 4 5 } & \mathbf { 5 . 5 6 } & \mathbf { 0 . 0 0 0 1 } \
\text { LNP } &  - 5.10 & 1.75 & - \mathbf { 2 . 9 1 } & \mathbf { 0 . 0 1 1 3 } \
\text { LNQ } &  12.4 & \mathbf { 3 . 2 } & \mathbf { 3 . 8 3 } & \mathbf { 0 . 0 0 1 7 } \
\text { LNR } & \mathbf { - 6 . 0 0 } & 1.5 & - 400 & \mathbf { 0 . 0 0 1 0 }
\end{array}$$
-The estimated value of a is

Accepted Answer

A)   0.916
B)   12.182
C)   2.50
D)   2.66

Question 9

Which of the following is an example of a time-series data set?

Accepted Answer

A)   amount of labor employed in each factory in the U.S. in 2010.
B)   amount of labor employed yearly in a specific factory from 1990 through 2010.
C)   average amount of labor employed at specific times of the day at a specific factory in 2010.
D)   All of the above are time-series data sets.

Question 10

Tests for statistical significance must be performed

Accepted Answer

A)   because the TRUE values of the intercept and slope parameters are random variables.
B)   because the ESTIMATED values of the intercept and slope parameters are not, in general, equal to the true values of the intercept and slope parameters.
C)   because the computed t-ratios are random variables and may be too large to provide evidence that b is not equal to zero.
D)   in order to determine whether or not the parameter estimates are far enough away from zero to conclude that the true parameter values are not equal to zero.
E)   both b and d

Question 11

A manager wishes to estimate an average cost equation of the following form:
  
where Q is the level of output. Letting Z = QS1U1P12S1S1P0 and using least-squares estimation, the manager obtains the following computer output:

$$\begin{array} { | c l l l l l | } 
\hline \text { DEPENDENT VARIABLE: } & \text { C } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ON F } \
\text { OBSERVATIONS: } & 28 & 0.7679 & 26.47 & 0.0001 & \
 \text { VARIABLE }  & \begin{array} { l } 
\text { PARAMETER } \
\text { ESTIMATE }
\end{array} & \begin{array} { l } 
\text { STANDARD } \
\text { ERROR }
\end{array}& \text { T-RATIO } & \text { P-VALUE } \
\text { INTERCEPT }&  200 & 38.00 & 5.26 & 0.0001 \
\text { Q }   & - 12.00 & 4.36 & - 2.75 & 0.0111 \
 \text { Z } & 0.50 & 0.16 & 3.13 & 0.0046 \
\hline
\end{array}$$
-The value of R2 indicates that _______ of the total variation in C is explained by the regression equation.

Accepted Answer

A)   0.7679%
B)   76.79%
C)   7.679%
D)   7679%

Question 12

A manager wishes to estimate an average cost equation of the following form:
  
where Q is the level of output. Letting Z = QS1U1P12S1S1P0 and using least-squares estimation, the manager obtains the following computer output:

$$\begin{array} { | c l l l l l | } 
\hline \text { DEPENDENT VARIABLE: } & \text { C } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ON F } \
\text { OBSERVATIONS: } & 28 & 0.7679 & 26.47 & 0.0001 & \
 \text { VARIABLE }  & \begin{array} { l } 
\text { PARAMETER } \
\text { ESTIMATE }
\end{array} & \begin{array} { l } 
\text { STANDARD } \
\text { ERROR }
\end{array}& \text { T-RATIO } & \text { P-VALUE } \
\text { INTERCEPT }&  200 & 38.00 & 5.26 & 0.0001 \
\text { Q }   & - 12.00 & 4.36 & - 2.75 & 0.0111 \
 \text { Z } & 0.50 & 0.16 & 3.13 & 0.0046 \
\hline
\end{array}$$
-When output is 20 units, what is average cost?

Accepted Answer

A)   $160
B)   $200
C)   $280
D)   $340
E)   $360

Question 13

In a linear regression equation Y = a + bX, the fitted or predicted value of Y is

Accepted Answer

A)   the value of Y obtained by substituting specific values of X into the sample regression equation.
B)   the value of X associated with a particular value of Y.
C)   the value of X that the regression equation predicts.
D)   the values of the parameters predicted by the estimators.
E)   the value of Y associated with a particular value of X in the sample.

Question 14

If an analyst believes that more than one explanatory variable explains the variation in the dependent variable, what model should be used?

Accepted Answer

A)   a simple linear regression model
B)   a multiple regression model
C)   a nonlinear regression model
D)   a log-linear model

Question 15

Refer to the following computer output from estimating the parameters of the nonlinear model
 $$\begin{array} { r l l l l l } 
\text { DEPENDENT VARIAELE: } & \text { LNY } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \
\text { OESERVATIONS: } & \text { 32 } & \mathbf { 0 . 7 7 5 6 } & \mathbf { 3 2 . 4 4 } & \mathbf { 0 . 0 0 0 1 } & \\
&  \text { PARAMETER } & \text { STANDARD } & & \
\text { VARIAELE }  & \text { ESTMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \

\text { INTEREEPT } & \mathbf { - 0 . 5 9 3 1 } & \mathbf { 0 . 3 2 } & \mathbf { - 2 . 1 7 } & \mathbf { 0 . 0 3 9 0 } \
\text { LNRR } & \mathbf { 4 . 6 5 } & 1.36 & \mathbf { 3 . 4 3 } & \mathbf { 0 . 0 0 1 9 } \
\text { LNS } & \mathbf { - 0 . 4 4 } & \mathbf { 0 . 2 4 } & - 1.83 & \mathbf { 0 . 0 7 7 4 } \
\text { LNT } & \mathbf { 8 . 2 8 } & \mathbf { 4 . 6 } & \mathbf { 1 . 8 0 } & \mathbf { 0 . 0 8 2 6 }
\end{array}$$
-If S increases by 8% (all other things constant), Y will

Accepted Answer

A)   decrease by 3.52%.
B)   decrease by 0.44%.
C)   decrease by 4.4%.
D)   increase by 0.44%.
E)   decrease by 2.4%.

Question 16

A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results:
 $$\begin{array} { c l l l l l } 
\text { DEPENDENT VARIAELE: } & \text { T } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \
\text { OESERVATIONS: } & 27 & \mathbf { 0 . 7 7 9 3 } & 42.38 & \mathbf { 0 . 0 0 0 1 } & \
& & \text { PARAMETER } & \text { STANDARD } & & \
\text { VARIAELE } & & \text { ESTMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \
\text { INTERCEPT } & & 5150.43 & 1740.72 & \mathbf { 2 . 9 6 } & \mathbf { 0 . 0 0 6 8 } \
\text { G } & & - 480.92 & 130.65 & - \mathbf { 3 . 6 8 } & \mathbf { 0 . 0 0 1 2 } \
\text { U } & & 211.0 & 75.0 & \mathbf { 2 . 8 1 } & \mathbf { 0 . 0 0 9 5 }
\end{array}$$
-Hiring one more guard per week will decrease the losses due to theft at the warehouse by _________ per week.

Accepted Answer

A)   $5,150
B)   $211
C)   $130
D)   $480.92

Question 17

In a regression equation, the ______ captures the effects of factors that might influence the dependent variable but aren't used as explanatory variables.

Accepted Answer

A)   intercept
B)   slope parameter
C)   R-square
D)   random error term

Question 18

Refer to the following computer output from estimating the parameters of the nonlinear model
 $$\begin{array} { r l l l l l } 
\text { DEPENDENT VARIAELE: } & \text { LNY } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \
\text { OESERVATIONS: } & \text { 32 } & \mathbf { 0 . 7 7 5 6 } & \mathbf { 3 2 . 4 4 } & \mathbf { 0 . 0 0 0 1 } & \\
&  \text { PARAMETER } & \text { STANDARD } & & \
\text { VARIAELE }  & \text { ESTMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \

\text { INTEREEPT } & \mathbf { - 0 . 5 9 3 1 } & \mathbf { 0 . 3 2 } & \mathbf { - 2 . 1 7 } & \mathbf { 0 . 0 3 9 0 } \
\text { LNRR } & \mathbf { 4 . 6 5 } & 1.36 & \mathbf { 3 . 4 3 } & \mathbf { 0 . 0 0 1 9 } \
\text { LNS } & \mathbf { - 0 . 4 4 } & \mathbf { 0 . 2 4 } & - 1.83 & \mathbf { 0 . 0 7 7 4 } \
\text { LNT } & \mathbf { 8 . 2 8 } & \mathbf { 4 . 6 } & \mathbf { 1 . 8 0 } & \mathbf { 0 . 0 8 2 6 }
\end{array}$$
-The nonlinear relation can be transformed into the following linear regression model:

Accepted Answer

A)    Y=ln⁡(aRbScTd) Y = \ln \left( a R ^ { b } S ^ { c } T ^ { d } \right) Y=ln(aRbScTd)  
B)    ln⁡Y=ln⁡(aRbScTd) \ln Y = \ln \left( a R ^ { \mathrm { b } } S ^ { \mathrm { c } } T ^ { \mathrm { d } } \right) lnY=ln(aRbScTd)  
C)    ln⁡Y=ln⁡a⋅ln⁡R⋅ln⁡S⋅ln⁡T\ln Y = \ln a \cdot \ln R \cdot \ln S \cdot \ln TlnY=lna⋅lnR⋅lnS⋅lnT 
D)    ln⁡Y=ln⁡a+bln⁡R+cln⁡S+dln⁡T\ln Y = \ln a + b \ln R + c \ln S + d \ln TlnY=lna+blnR+clnS+dlnT

Question 19

Refer to the following nonlinear model which relates W to P, Q, and R:
 $W = a P ^ { b } Q ^ { c } R ^ { d }$ 
The computer output form the regression analysis is:
 $$\begin{array} { r l l l l l } 
\text { DEPENDENTVARIAELE: } & \text { LNW } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \
\text { OESERVATIONS: } & \text { 19 } & \mathbf { 0 . 9 0 2 3 } & 43.12 & \mathbf { 0 . 0 0 0 1 } & \\
&  \text { PARAMETER } & \text { STANDARD } & & \
\text { VARIAELE }  & \text { ESTMMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \
\text { INTERCEPT } & \mathbf { 2 . 5 0 } & \mathbf { 0 . 4 5 } & \mathbf { 5 . 5 6 } & \mathbf { 0 . 0 0 0 1 } \
\text { LNP } &  - 5.10 & 1.75 & - \mathbf { 2 . 9 1 } & \mathbf { 0 . 0 1 1 3 } \
\text { LNQ } &  12.4 & \mathbf { 3 . 2 } & \mathbf { 3 . 8 3 } & \mathbf { 0 . 0 0 1 7 } \
\text { LNR } & \mathbf { - 6 . 0 0 } & 1.5 & - 400 & \mathbf { 0 . 0 0 1 0 }
\end{array}$$
-The nonlinear relation can be transformed into the following linear regression model:

Accepted Answer

A)    W=ln⁡(aPbQcRh) W = \ln \left( a P ^ { b } Q ^ { c } R ^ { \mathrm { h } } \right) W=ln(aPbQcRh)  
B)    ln⁡W=ln⁡(aPbQcRd) \ln W = \ln \left( a P ^ { \mathrm { b } } Q ^ { \mathrm { c } } R ^ { \mathrm { d } } \right) lnW=ln(aPbQcRd)  
C)    ln⁡W=ln⁡a⋅ln⁡P⋅ln⁡Q⋅ln⁡R\ln W = \ln a \cdot \ln P \cdot \ln Q \cdot \ln RlnW=lna⋅lnP⋅lnQ⋅lnR 
D)    ln⁡W=ln⁡a+bln⁡P+cln⁡Q+dln⁡R\ln W = \ln a + b \ln P + c \ln Q + d \ln RlnW=lna+blnP+clnQ+dlnR

Question 20

A parameter estimate is said to be statistically significant if there is sufficient evidence that the

Accepted Answer

A)   sample regression equals the population regression.
B)   parameter estimated from the sample equals the true value of the parameter.
C)   value of the t-ratio equals the critical value.
D)   true value of the parameter does not equal zero.

Exam 4: Basic Estimation Techniques

In the linear model Y=a+bX+cZY = a + b X + c ZY=a+bX+cZ , a test of the hypothesis that parameter c equals zero is