Deck 4: Basic Estimation Techniques

Question 1

In a linear regression equation of the form Y = a + bX, the slope parameter b shows

A) $\Delta$ X / $\Delta$ Y.
B) $\Delta$ Y / $\Delta$ X.
C) $\Delta$ Y / $\Delta$ b.
D) $\Delta$ X / $\Delta$ b.
E) none of the above

Answer 1

$\Delta$ Y / $\Delta$ X.

Question 2

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

A) amount of labor employed in each factory in the U.S. in 2007.
B) amount of labor employed yearly in a specific factory from 1987 through 2007.
C) average amount of labor employed at specific times of the day at a specific factory in 2007.
D) All of the above are time-series data sets.

Answer 2

amount of labor employed yearly in a specific factory from 1987 through 2007.

Question 3

In the linear model

, a test of the hypothesis that parameter c equals zero is

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

Answer 3

a t-test.

Question 4

refer to the following:
The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
?

-What is the critical value of t at the 1% level of significance?

A) 1.746
B) 2.120
C) 2.878
D) 2.921

Question 5

refer to the following:
The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
?

-Which of the following statements is correct at the 1% level of significance?

A) Both

And

Are statistically significant.
B) Neither

Nor

Is statistically significant.
C)

Is statistically significant, but

Is not.
D)

Is statistically significant, but

Is not.

Question 6

refer to the following:
The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
?

-The exact level of significance of

Is

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

Question 7

refer to the following:
The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
?

-If X equals 20, what is the predicted value of Y?

A) 186.42
B) 165.69
C) -186.42
D)-411.72

Question 8

refer to the following:
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:


-Which of the following is correct at the 1% level of significance?

A) The regression equation as a whole is statistically significant because the p-value of F is smaller than 0.01.
B) The estimates of the parameters a, b, and c are all statistically significant because the absolute values of their t-ratios exceed 2.797.
C) The estimates of the parameters a, b, and c are all statistically significant because the p- values for,

,

And

Are all less than 0.01.
D) The critical value of t is 2.797.
E) all of the above

Question 9

In the nonlinear function

, the parameter c measures

A) $\Delta$ Y / $\Delta$ 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 10

refer to the following computer output from estimating the parameters of the nonlinear model
The computer output from the regression analysis is:


-The nonlinear relation can be transformed into the following linear regression model:

A)
B)
C)
D)

Question 11

refer to the following computer output from estimating the parameters of the nonlinear model
The computer output from the regression analysis is:


-The estimated value of a is

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

Question 12

refer to the following computer output from estimating the parameters of the nonlinear model
The computer output from the regression analysis is:


-Which of the parameter estimates are statistically significant at the 90% level of confidence?

A) All the parameter estimates are statistically significant.
B) All parameter estimates except

And

Are statistically significant.
C)

Is not statistically significant, but all the rest of the parameter estimates are significant.
D)

Is not statistically significant, but all the rest of the parameter estimates are significant.

Question 13

refer to the following nonlinear model which relates W to P, Q, and R:

The computer output form the regression analysis is:


-The nonlinear relation can be transformed into the following linear regression model:

A)
B)
C)
D)

Question 14

refer to the following nonlinear model which relates W to P, Q, and R:

The computer output form the regression analysis is:


-Which of the parameter estimates are statistically significant at the 5% level of significance?

A) All the parameter estimates are statistically significant.
B) All parameter estimates except and are statistically significant.
C)

Is not statistically significant, but all the rest of the parameter estimates are significant.
D)

Is not statistically significant, but all the rest of the parameter estimates are significant.

Question 15

refer to the following nonlinear model which relates W to P, Q, and R:

The computer output form the regression analysis is:


-The estimated value of a is

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

Question 16

In a multiple regression model, the coefficients on the independent variables measure

A) the percent of the variation in the dependent variable explained by a change in that independent variable, all other influences held constant.
B) the change in the dependent variable from a one-unit change in that independent variable, all other influences held constant.
C) the change in that independent variable from a one-unit change in the dependent variable, all other influences held constant.
D) the change in the dependent variable explained by the random error, all other influences held constant.

Question 17

refer to the following:
A manager wishes to estimate an average cost equation of the following form:

where Q is the level of output. Letting Z = Q² and using least-squares estimation, the manager obtains the following computer output:


-Which of the parameter estimates are statistically significant at the 1% significance level?

A) All the parameter estimates are statistically significant.
B) All parameter estimates except are statistically significant.
C) is not statistically significant, but all the rest of the parameter estimates are significant.
D) is not statistically significant, but all the rest of the parameter estimates are significant.

Question 18

refer to the following:
A manager wishes to estimate an average cost equation of the following form:

where Q is the level of output. Letting Z = Q² and using least-squares estimation, the manager obtains the following computer output:


-When output is 40 units, what is average cost?

A) $200
B) $280
C) $360
D) $480
E) $520

Question 19

refer to the following:
A manager wishes to estimate an average cost equation of the following form:

where Q is the level of output. Letting Z = Q² and using least-squares estimation, the manager obtains the following computer output:


-When output is 20 units, what is average cost?

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

Question 20

A simple linear regression equation relates G and D as follows:
G = a + bD
-The explanatory variable is _______, and the dependent variable is ________.

Question 21

A simple linear regression equation relates G and D as follows:
G = a + bD
-The slope parameter is ______, and the intercept parameter _______.

Question 22

A simple linear regression equation relates G and D as follows:
G = a + bD
-When D is zero, G equals _______.

Question 23

A simple linear regression equation relates G and D as follows:
G = a + bD
-For each one-unit increase in D, the change in R is ______ units.

Question 24

The linear regression equation G = a + bD is estimated using 24 observations on R and W. The least-squares estimate of b is -22.5, and the standard error of the estimate is 8.36. Perform a t-test for statistical significance of
at the 1% level of significance.

-There are _____ degrees of freedom for the t-test.

Question 25

The linear regression equation G = a + bD is estimated using 24 observations on R and W. The least-squares estimate of b is -22.5, and the standard error of the estimate is 8.36. Perform a t-test for statistical significance of
at the 1% level of significance.

-The value of the t-statistic is _________. The critical t-value for the test is _________.

Question 26

The linear regression equation G = a + bD is estimated using 24 observations on R and W. The least-squares estimate of b is -22.5, and the standard error of the estimate is 8.36. Perform a t-test for statistical significance of
at the 1% level of significance.

-The parameter estimate _________ (is, is not) statistically significant at the 1% level.

Question 27

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-The equation of the sample regression line is: = __________________________.

Question 28

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-There are ______ degrees of freedom for the t-test. At the 5% level of significance, the critical t-value for the test is ______________.

Question 29

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-At the 5% level of significance, __________ (is, not) significant, and ________ (is, is not) significant.

Question 30

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-At the 2% level of significance, the critical t-value for a t-test is ___________. At the 2% level of significance, _________ (is, is not) significant, and _________ (is, is not) significant.

Question 31

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-The p-value for indicates that the exact level of significance is ______ percent, which is the probability of _________________________________________.

Question 32

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-At the 5% level of significance, the critical value of the F-statistic is _______. The model as a whole ___________(is, is not) significant at the 5% level.

Question 33

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-If X equals 240, the fitted (or predicted) value of Y is ____________________________.

Question 34

Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is


-The percentage of the total variation in Y that is NOT explained by the regression is ________.

Question 35

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-In order to estimate the parameters a, b, and c, the equation must be transformed into the form: ___________________________________.

Question 36

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-There are _______ degrees of freedom for the t-test. At the 1% level of significance, the critical t-value for the test is __________.

Question 37

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-At the 1% level of significance, _______ (is, is not) significant, _______ (is, is not) significant, and ________ (is, is not) significant.

Question 38

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-The estimated value of a is ______________.

Question 39

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-The p-value for indicates that the exact level of significance is _________ percent, which is the probability of _________________.

Question 40

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-At the 1% level of significance, the critical value of the F-statistic is _________. The model as a whole _________ (is, is not) significant at the 1% level.

Question 41

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-If R equals 12 and S equals 30, the fitted (or predicted) value of Y is _____________.

Question 42

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-The percentage of the total variation in the dependent variable NOT explained by the regression is _______________.

Question 43

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-If R increases by 14%, Y will increase by ________ percent.

Question 44

4-4F Suppose Y is related to R and S in the following nonlinear way:

Twenty-six observations are used to obtain the following regression results:
‪
-A 6.87% increase in Y will occur if S ________________ (increases, decreases) by _______ percent.

Question 45

4-5F Seventy-five data point on H, U, V, and W are employed to estimate the parameters in the linear relation
. The computer output from the regression analysis is shown below:

-The estimated sample regression line is _________________________________.

Question 46

4-5F Seventy-five data point on H, U, V, and W are employed to estimate the parameters in the linear relation
. The computer output from the regression analysis is shown below:

-At the 2% level of significance, ‪ _________ (is, is NOT) significant,‪ _________ (is, is NOT) significant,‪ _________ (is, is NOT) significant, and‪ _________ (is, is NOT) significant.

Question 47

4-5F Seventy-five data point on H, U, V, and W are employed to estimate the parameters in the linear relation
. The computer output from the regression analysis is shown below:

-At the 4% level of significance, __________ (is, is not) significant, ________ (is, is not) significant, ________ (is, is not) significant, and ________ (is, is not) significant.

Question 48

4-5F Seventy-five data point on H, U, V, and W are employed to estimate the parameters in the linear relation
. The computer output from the regression analysis is shown below:

-The p-value for indicates that the exact level of significance is ______ percent, which is the probability of _______________________________.

Question 49

4-5F Seventy-five data point on H, U, V, and W are employed to estimate the parameters in the linear relation
. The computer output from the regression analysis is shown below:

-If U equals 4, V equals 8, and W equals 10, the fitted (or predicted) value of H is ____________.

Question 50

4-5F Seventy-five data point on H, U, V, and W are employed to estimate the parameters in the linear relation
. The computer output from the regression analysis is shown below:

-The percentage of the total variation in H explained by the regression is ________ percent.