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ECO 391 (Fall 2022)
Exam 2 Directions: ●
You have 60 minutes to complete the exam and it is out of 100 points. ●
Multiple choice 1 to 42 are worth 2.38 points per question. Good Luck!!! 1.
The table below shows a portion of regression results.
1
SS
MS
F
Significance
F
Regression
17248773
17248773
926.170433
9.80086E-68
Residual
2923930
18623.76
Total
20172703
What is the R
2
value?
a.
0.56
b.
0.66
c.
0.76
d.
0.86
2.
Which of the following corresponds to the explained part of the variation in the dependent variable?
a.
The total sum of squares
b.
The regression sum of squares
c.
The residual sum of squares
d.
The degrees of freedom
3.
A model has unexplained variation of 153.47 and total variation of 1234.50. What is the R
2
value of this model?
a.
0.1243
b.
0.8756
c.
0.95
d.
1.04
4.
A researcher is interested in the determinants of monthly consumption of natural gas in North Carolina. She estimates a simple model with only mean monthly temperature as the independent variable. What does the R
2
of this model represent?
a.
The variance of the coefficient on mean temperature
b.
The percent of variation in gas consumption explained by variations in mean temperature
c.
The expected increase in gas consumption associated with a one unit increase in mean temperature
d.
The mean difference between the predicted level of gas consumption and the actual value
2
5.
Consider the following sample regression equation: Y
bar
¿
27
−
5
∗
x
1
+
2
∗
x
2
. When x
1
is equal to 0 and x
2
is equal to 1, the dependent variable is equal to 19. What is the residual (the error) for this observation?
a.
-5
b.
27
c.
-10
d.
4
6.
Which of the following variables is categorical?
a.
Time
b.
Cost
c.
Sex
d.
Weight
7.
A researcher models gas
=
B
0
+
β
1
∗
high
+
β
2
∗
low
. What is the predicted change in gas if both high and low increase by 1 unit?
a.
β
0
b.
β
0
+
β
1
+
β
2
c.
β
0
+
β
1
d.
β
1
+
β
2
8.
The results of estimating the model gas
=
B
0
+
β
1
∗
high
+
β
2
∗
low
is given below, where high is mean maximum temp and low is mean minimum temp.
Coefficients
Standard Error
t Stat
P-value
Intercept
64269
9621.358767
6.6799
3.67391E-09
Mean Maximum Temp
-2148
787.7000993
-2.727
0.007946215
Mean Minimum Temp
1260.9
773.3760344
1.6303
0.107224631
What is the estimated value of β
1
?
a.
64,269
b.
-2.727
c.
-2,148 d.
1.6303
9.
Consider the sample regression equation ^
y
=
15
+
2
x
1
+
7
x
2
−
x
3
. What is the predicted value of the dependent variable when x
1
=
2
, x
2
=
1
, and x
3
=
4
?
a.
15
3
b.
22
c.
26
d.
31
10.
Consider the sample regression equation ^
y
=
15
+
2
x
1
+
7
x
2
−
x
3
. What is the predicted change in
Yhat when x
1
increases by 1 unit, x
2
does not change, and x
3
increases by 1 unit?
a.
Decrease 2 units
b.
Decrease 1 unit
c.
Increase 1 unit
d.
Increase 2 units
11.
Consider the sample regression equation ^
y
=
15
+
2
x
1
+
7
x
2
−
x
3
. What is the value of the residual
when x
1
is 0, x
2
is 0, x
3
is 5, and Y is 20?
a.
10
b.
15
c.
20
d.
25
12.
What is one advantage of using dummy variables?
a.
They can take any possible value, making it easier to work with
b.
They are simpler to add to your model than other variables.
c.
They allow you to capture qualitative measures.
d.
They have no advantage over other variables.
13.
A researcher estimates the model
crime
=
β
0
+
β
1
∗
education
+
β
2
∗
wage
+
β
3
∗
youth
+
β
4
Expenditure
+
ε
. She obtains the results below.
Coefficients
Intercept
-111.688723
Education
1.66861011
Wage
0.00332358
Youth
-0.89949622
Expenditure
0.79326242
Increases in which variables are associated with increases in crime?
a.
Education
b.
Education, wage
4
c.
Education, wage, youth
d.
Education, wage, expenditure
14.
In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. Thus, the coefficient of determination is __________. a.
0.139
b.
0.122
c.
0.878
d.
0.731
15.
A researcher estimates the model
crime
=
β
0
+
β
1
∗
education
+
β
2
∗
wage
+
β
3
∗
youth
+
β
4
∗
Expenditure
+
ε
. She obtains the results below.
Coefficients
Standard Error
t Stat
P-value
Intercept
-111.688723
72.60820393
-1.53824
0.131491
Education
1.66861011
3.305592294
0.504784
0.616349
Wage
0.00332358
0.065738859
0.050557
0.959918
Youth
0.89949622
0.332354675
2.706435
0.009789
Expenditure
0.79326242
0.172211478
4.606327
0.000037
What is the predicted increase in the crime rate associated with a one unit increase in education, holding constant wage, youth, and expenditure?
a.
-111.69
b.
1.67
c.
72.61
d.
3.31
16.
A researcher estimates the model
crime
=
β
0
+
β
1
∗
education
+
β
2
∗
wage
+
β
3
∗
youth
+
β
4
∗
Expenditure
+
ε
. She obtains the results below.
Coefficients
Standard Error
t Stat
P-value
Intercept
-111.688723
72.60820393
-1.53824
0.131491
5
Education
1.66861011
3.305592294
0.504784
0.616349
Wage
0.00332358
0.065738859
0.050557
0.959918
Youth
0.89949622
0.332354675
2.706435
0.009789
Expenditure
0.79326242
0.172211478
4.606327
0.000037
The estimate for which coefficients are significant at the 5% level?
a.
β
1
, β
2
b.
β
1
, β
3
c.
β
3
,β
4
d.
β
2
,β
4
17.
Consider the sample regression equation ^
y
=
39
+
1.5
∗
x
. If x increases by 4 units, what is the predicted change in Yhat?
a.
1.5
b.
6
c.
39
d.
45
18.
A research wants to estimate the linear regression model y
=
β
0
+
β
1
∗
x
+
ε
to study the relationship between salary and years of education among workers in middle-age. Which variable should be used as the Y?
a.
Salary
b.
Years of education c.
Workers
d.
Workers in middle-age
19.
A researcher models the crime rate as a function of the average wage within a state. Below is a portion of her results.
Regression Statistics
Multiple R
0.4248
R Square
0.1805
Adjusted R Square
0.1622
Standard Error
26.445
6
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