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Mathematics
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Social Statistics Managing
Quiz 10: Above and Beyond: The Logic of Controlling and The Power of Nested Regression Models
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Question 1
Multiple Choice
Which of the following is not the same as the others?
Question 2
Multiple Choice
In Model 1, Independent Variable A has a statistically significant effect. In Model 2, we add Independent Variable B, which has a statistically significant effect, and the effect of Independent Variable A moves closer to zero and loses its statistical significance. What might we have here?
Question 3
Multiple Choice
What symbol is used to signify "this independent variable is not in this model, but it will be introduced in a subsequent model?
Question 4
Multiple Choice
When you have a first regression model, then a second regression model with an additional independent variable, then a third regression model with yet another additional independent variable, we call these a set of:
Question 5
Multiple Choice
The smallest number of regression models you need to have nested modeling is:
Question 6
Multiple Choice
We run a regression model using GSS2006 data and find out that the older one is, the higher he/she scores on an index of religiosity (where 0=not religious up to 9=very religious) . Then, we hypothesize that, because women outlive men, and because women are typically more religious than men are, part of this age effect is actually due to sex. We run a second model in which we add a variable for sex:
Independent Variable
Model 1
Model 2
Age (in years)
.
03
∗
∗
∗
.
03
∗
∗
∗
Sex
(
F
=
0
,
M
=
1
)
−
−
−
−
.
93
∗
∗
∗
Constant
4.23
4.65
R-Squared
.
04
.
07
n
2912
2912
\begin{array}{lcc}\text { Independent Variable } & \text { Model 1 } & \text { Model 2 } \\\text { Age (in years) } & .03 * * * & .03 * * * \\\text { Sex }(\mathrm{F}=0, \mathrm{M}=1) & --- & -.93 * * * \\\text { Constant } & 4.23 & 4.65 \\\text { R-Squared } & .04 & .07 \\\mathrm{n} & 2912 & 2912\end{array}
Independent Variable
Age (in years)
Sex
(
F
=
0
,
M
=
1
)
Constant
R-Squared
n
Model 1
.03
∗
∗
∗
−
−
−
4.23
.04
2912
Model 2
.03
∗
∗
∗
−
.93
∗
∗
∗
4.65
.07
2912
Which of the following is the most appropriate interpretation of what is going on here?
Question 7
Multiple Choice
Here are two models made using GSS2006 data. The dependent variable is hours of television watched per day:
Independent Variable
Model 1
Model
2
Age (in years)
.
0
2
∗
∗
∗
.
00
Working or Retired
−
−
1.3
2
∗
∗
∗
Constant
1.70
2.51
R-Squared
.
03
.
06
n
1523
1523
\begin{array}{lcc}\text { Independent Variable } & \text { Model 1 } & \text { Model } 2 \\\text { Age (in years) } & .02^{* * *} & .00 \\\text { Working or Retired } & -- & 1.32^{* * *} \\\text { Constant } & 1.70 & 2.51 \\\text { R-Squared } & .03 & .06 \\\mathrm{n} & 1523 & 1523\end{array}
Independent Variable
Age (in years)
Working or Retired
Constant
R-Squared
n
Model 1
.0
2
∗∗∗
−
−
1.70
.03
1523
Model
2
.00
1.3
2
∗∗∗
2.51
.06
1523
Which of the following pairs of people watches the same hours of television?
Question 8
Multiple Choice
We hypothetically observe that the higher one's education, the happier one is. We hypothesize that this is actually because of income: people with higher education tend to make higher incomes, and it is these higher incomes, not education, that causes the higher happiness. Here are hypothetical models (using a dependent variable where 0=not at all happy, up to 10=very happy) :
Independent Variable
Model 1
Model
2
Education (in years)
.
3
5
∗
∗
∗
?
?
?
Income (in thousands of dollars)
−
−
−
.
0
3
∗
∗
∗
Constant
.
50
−
2.50
R-Squared
.
10
.
15
n
1000
1000
\begin{array}{lcc}\text { Independent Variable } & \text { Model 1 } & \text { Model } 2 \\\text { Education (in years) } & .35^{* * *} & ? ? ? \\\text { Income (in thousands of dollars) } & --- & .03^{* * *} \\\text { Constant } & .50 & -2.50 \\\text { R-Squared } & .10 & .15 \\\mathrm{n} & 1000 & 1000\end{array}
Independent Variable
Education (in years)
Income (in thousands of dollars)
Constant
R-Squared
n
Model 1
.3
5
∗∗∗
−
−
−
.50
.10
1000
Model
2
???
.0
3
∗∗∗
−
2.50
.15
1000
To support the hypothesis, what is the most likely number that would go in the place of the "???" in Model 2?
Question 9
Multiple Choice
In the "Attitudes toward Inequality" example in the textbook, which group's difference from whites is most robust?
Question 10
Multiple Choice
In the "Attitudes toward Inequality" example in the textbook, what happens to the effect of political party once income is controlled for?
Question 11
Multiple Choice
In Model 1, Independent Variable A does not have a statistically significant effect. In Model 2, we add Independent Variable B, which has a statistically significant effect, and the effect of Independent Variable A gets larger and is now statistically significant. Independent Variable B is called:
Question 12
Multiple Choice
The "BMI, Internet Use, and Age" example in the textbook offered an example of a(n) _______________ relationship.
Question 13
Multiple Choice
What statistical test do we use to see if a second regression model is better than the first regression model?
Question 14
Multiple Choice
Someone hypothetically comes to you with some regression results that are confusing him:
Independent Variable:
Model 1
Model
2
Education (in years)
3.4
7
∗
∗
∗
3.47
Uses a computer at work
(
Y
=
1
,
N
=
0
)
−
−
7.80
Constant
−
20.45
−
24.20
R-Squared
.
14
.
14
n
1000
100
\begin{array}{lcc}\text { Independent Variable: } & \text { Model 1 } & \text { Model } 2 \\\text { Education (in years) } & 3.47^{* * *} & 3.47 \\\text { Uses a computer at work }(Y=1, N=0) & -- & 7.80 \\\text { Constant } & -20.45 & -24.20 \\\text { R-Squared } & .14 & .14 \\n & 1000 & 100\end{array}
Independent Variable:
Education (in years)
Uses a computer at work
(
Y
=
1
,
N
=
0
)
Constant
R-Squared
n
Model 1
3.4
7
∗∗∗
−
−
−
20.45
.14
1000
Model
2
3.47
7.80
−
24.20
.14
100
He is confused by what happens to the effect of education between Model 1 and Model 2: the value of the slope is the same, but it is no longer statistically significant. What is the most likely explanation for this?
Question 15
Multiple Choice
Ainsworth-Darnell and Downey use which dataset for their study of student grades?
Question 16
Multiple Choice
The explanation that Ainsworth-Darnell and Downey refute with their statistical analysis of racial differences in grades is called:
Question 17
Multiple Choice
In the Ainsworth-Darnell and Downey research on racial differences in grades, which of the following nested stories is not present?
Question 18
Multiple Choice
With regard to the expectation that black students have more negative attitudes toward school than white students, Ainsworth-Darnell and Downey provide findings that _________ this expectation.
Question 19
Multiple Choice
Regarding the interconnections between race and social class in the Ainsworth-Darnell and Downey article about grades, which of the following statements best captures their overall findings: