USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 22 – 30. A researcher wished t
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Question
USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 22 – 30.
A researcher wished to know the impact of agricultural employment on per capita income in developed countries. She gathered and recorded agricultural employment (in percent) and per capita incomes (in thousands of U.S. dollars) for 10 countries. Using the output below and a = .05, answer the following questions.
Regression Statistics
Multiple R
0.682
R Square
0.465
Adjusted R Square
0.398
Standard Error
2.658
Observations
ANOVA
df
SS
MS
F
Significance F
Regression
1
49.072
49.072
6.945
0.030
Residual
8
56.528
7.066
Total
9
105.6
Coefficients
Standard Error
t Stat
P-value
Intercept
24.577
3.07
8.01
4.33E-5
Ag Empl
-1.095
0.42
-2.64
2.99E-2
The correlation coefficient indicates that Agricultural Employment and Per Capita Income are
Select one:
a. Not at all correlated
b. Fairly highly correlated
c. Only weakly correlated
In regression, a significant B coefficient for an X variable (say X1) tells a researcher
Select one:
a. The amount that X1 changes in response to the other Xs
b. The amount and direction that Y changes in response to a change in X1
c. The percent of variation in Y not explained by X1
d. The percent of the variation in Y explained by X1
The negative sign of the regression coefficient for Ag Empl means that
Select one:
a. Countries with higher rates of agricultural employment have higher per capita incomes.
b. Countries with higher rates of agricultural employment have lower per capita incomes.
c. Ag employment and per capita income are not correlated.
d. The Y-intercept is negative.
The P-value for the Ag Empl term in regular notation, not in scientific notation, is
Select one:
a. 0.0299
b. 0.00299
c. 299
d. 0.299
Which of the following is significant?
Select one:
a. The intercept
b. The slope coefficient
c. Both the intercept and the slope coefficient
d. Neither the intercept nor the slope coefficient
The correct regression equation is
Select one:
a. PER CAP INC = – 1.095 + 24.58 AG EMPL
b. PER CAP INC = 1.095 – 24.58 AG EMPL
c. PER CAP INC = 24.58 – 1.095 AG EMPL
d. AG EMPL = 24.58 – 1.095 PER CAP INC
The correct regression equation explains about
Select one:
a. 46% of the variation in PER CAP INCOME
b. 46% of the variation in AG EMPL
c. Nothing because the coefficients are insignificant
d. .03 (or 3%) of the variation in PER CAP INC
One can know that the overall regression equation is significant because
Select one:
a. The R2 is high
b. The Significance-f is high
c. The Significance-f is less than alpha
d. The coefficient t-values are significant
Which of the following is an appropriate interpretation of the equation resulting from this study?
Select one:
a. Reducing agricultural employment by 1% will result in about a $1095 gain in per capita income
b. All of these interpretations are correct.
c. Countries whose agricultural sectors are more efficient can reallocate their productive resources to other uses such as manufacturing.
d. Shifting labor resources from agriculture to manufacturing increases countries’ per capita income.
What is the estimated per capita income for a country whose agricultural employment rate is 7.5%?
Select one:
a. $32,790
b. $34,410
c. $19,415
d. $16,370
10
Regression Statistics
Multiple R
0.682
R Square
0.465
Adjusted R Square
0.398
Standard Error
2.658
Observations
ANOVA
df
SS
MS
F
Significance F
Regression
1
49.072
49.072
6.945
0.030
Residual
8
56.528
7.066
Total
9
105.6
Coefficients
Standard Error
t Stat
P-value
Intercept
24.577
3.07
8.01
4.33E-5
Ag Empl
-1.095
0.42
-2.64
2.99E-2
The correlation coefficient indicates that Agricultural Employment and Per Capita Income are
Select one:
a. Not at all correlated
b. Fairly highly correlated
c. Only weakly correlated
In regression, a significant B coefficient for an X variable (say X1) tells a researcher
Select one:
a. The amount that X1 changes in response to the other Xs
b. The amount and direction that Y changes in response to a change in X1
c. The percent of variation in Y not explained by X1
d. The percent of the variation in Y explained by X1
The negative sign of the regression coefficient for Ag Empl means that
Select one:
a. Countries with higher rates of agricultural employment have higher per capita incomes.
b. Countries with higher rates of agricultural employment have lower per capita incomes.
c. Ag employment and per capita income are not correlated.
d. The Y-intercept is negative.
The P-value for the Ag Empl term in regular notation, not in scientific notation, is
Select one:
a. 0.0299
b. 0.00299
c. 299
d. 0.299
Which of the following is significant?
Select one:
a. The intercept
b. The slope coefficient
c. Both the intercept and the slope coefficient
d. Neither the intercept nor the slope coefficient
The correct regression equation is
Select one:
a. PER CAP INC = – 1.095 + 24.58 AG EMPL
b. PER CAP INC = 1.095 – 24.58 AG EMPL
c. PER CAP INC = 24.58 – 1.095 AG EMPL
d. AG EMPL = 24.58 – 1.095 PER CAP INC
The correct regression equation explains about
Select one:
a. 46% of the variation in PER CAP INCOME
b. 46% of the variation in AG EMPL
c. Nothing because the coefficients are insignificant
d. .03 (or 3%) of the variation in PER CAP INC
One can know that the overall regression equation is significant because
Select one:
a. The R2 is high
b. The Significance-f is high
c. The Significance-f is less than alpha
d. The coefficient t-values are significant
Which of the following is an appropriate interpretation of the equation resulting from this study?
Select one:
a. Reducing agricultural employment by 1% will result in about a $1095 gain in per capita income
b. All of these interpretations are correct.
c. Countries whose agricultural sectors are more efficient can reallocate their productive resources to other uses such as manufacturing.
d. Shifting labor resources from agriculture to manufacturing increases countries’ per capita income.
What is the estimated per capita income for a country whose agricultural employment rate is 7.5%?
Select one:
a. $32,790
b. $34,410
c. $19,415
d. $16,370
10
Explanation / Answer
1)b. Fairly highly correlated(Multiple R = 0.682)
2) b. The amount and direction that Y changes in response to a change in X1
3) b. Countries with higher rates of agricultural employment have lower per capita incomes.
4) a. 0.0299
5) c. Both the intercept and the slope coefficient
6) c. PER CAP INC = 24.58 – 1.095 AG EMPL
7) a. 46% of the variation in PER CAP INCOME(R squared value)
8) c. The Significance-f is less than alpha
9) b. All of these interpretations are correct.
10) PER CAP INC = 24.58 – 1.095 * 7.5 = 16.3675
d. $16,370
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