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) The smallest number of regression models you need to have nested modeling is:) 1 b.) 2 c.) 3 d.) 4 2.
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) 0.03*** 0.03***
Sex (, ) --- -0.93***
Constant 4.23 4.65
R-Squared 0.04 0.07
n 2912 2912
Which of the following is the most appropriate interpretation of what is going on here?
a.) Sex clearly has a larger effect than age, so our hypothesis is supported.
b.) The value of R-Squared rises, so our hypothesis is supported.
c.) The effect of age does not change, so our hypothesis is not supported.
d.) The constant increases, so our hypothesis is not supported.
5.) 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 at all happy, up to happy):
Independent Variable Model 1 Model 2
Education (in years) 0.35*** ???
Income (in thousands of dollars) --- 0.03***
Constant 0.50 -2.50
R-Squared 0.10 0.15
n 1000 1000
To support the hypothesis, what is the most likely number that would go in the place of the “???” in Model 2?
a.) .03
b.) .20**
c.) .35*
d.) .50***
6.) 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?
a.) an intervening relationship
b.) a dependent relationship
c.) an independent relationship
d.) a controlling relationship
7.)
a.) We are interested in explaining the number of hours per week that the CRMJ 321 students spend playing videogames during the school year (rvidsch). Perhaps, we think, this variable can be explained by some students’ political views! We use our political variables to predict videogame playing and end up with the following regression (Model 1):
. regress rvidsch abort deathpen
Source | SS df MS Number of obs = 109
-------------+------------------------------ F( 2, 106) = 2.13
Model | 250.659437 2 125.329719 Prob > F = 0.1236
Residual | 6230.07909 106 58.7743311 R-squared = 0.0387
-------------+------------------------------ Adj R-squared = 0.0205
Total | 6480.73853 108 60.0068383 Root MSE = 7.6664
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rvidsch | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
abort | -.8708947 .4901819 -1.78 0.078 -1.842728 .1009386
deathpen | .484386 .4736684 1.02 0.309 -.4547077 1.42348
_cons | 4.801033 1.543066 3.11 0.002 1.741755 7.860312
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What can we conclude from our results? Interpret the coefficients and discuss how much of the variance of videogame playing is accounted for by political factors.
b.) Undeterred, we press on, suggesting that perhaps political views are not the only answer. Below is a Model 2, multiple regression explaining school year videogame playing.
. regress rvidsch age height urban rvidsum rtvsch abort deathpen
Source | SS df MS Number of obs = 107
-------------+------------------------------ F( 7, 99) = 25.19
Model | 4116.453 7 588.064715 Prob > F = 0.0000
Residual | 2311.36943 99 23.3471659 R-squared = 0.6404
-------------+------------------------------ Adj R-squared = 0.6150
Total | 6427.82243 106 60.6398342 Root MSE = 4.8319
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rvidsch | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.5397808 .1949932 -2.77 0.007 -.9266896 -.1528719
height | .3511119 .1171413 3.00 0.003 .1186781 .5835456
urban | -.975658 1.214456 -0.80 0.424 -3.385401 1.434085
rvidsum | .4494623 .0414731 10.84 0.000 .3671706 .531754
rtvsch | .1787645 .0532984 3.35 0.001 .073009 .28452
abort | -.7029951 .3151186 -2.23 0.028 -1.328259 -.0777314
deathpen | .172909 .3069888 0.56 0.575 -.4362233 .7820413
_cons | -11.53183 9.254303 -1.25 0.216 -29.89437 6.830718
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Discuss this model as compared to the last model. First, does it do a better job explaining videogame playing? How do we know? Write out the equation.
c.) Interpret the results of each variable on hours of video games played per week for Model 2. Be specific. Do the results surprise you? To aid in your discussion, below is a table depicting all of the variables used in the analysis:
Variable | Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
rvidsch | 5.191589 7.787158 0 35
age | 21.7037 3.054824 18 43
height | 68.89815 4.224295 56 80
urban | 0.212963 0.4113103 0 1
rvidsum | 6.925926 11.8416 0 60
-------------+--------------------------------------------------------
rtvsch | 9.634259 11.1978 0 100
abort | 1.138889 1.506735 0 (choice) 4 (life)
deathpen | 2.62037 1.545071 0 (con) 4 (pro)
d.)
In this final model (Model 3), we remove height from the equation.
. regress rvidsch age urban rvidsum rtvsch abort deathpen
Source | SS df MS Number of obs = 107
-------------+------------------------------ F( 6, 100) = 25.83
Model | 3906.70149 6 651.116916 Prob > F = 0.0000
Residual | 2521.12094 100 25.2112094 R-squared = 0.6078
-------------+------------------------------ Adj R-squared = 0.5842
Total | 6427.82243 106 60.6398342 Root MSE = 5.0211
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rvidsch | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.5933422 .2017752 -2.94 0.004 -.9936586 -.1930259
urban | -.524767 1.252287 -0.42 0.676 -3.009269 1.959735
rvidsum | .4774664 .0419891 11.37 0.000 .3941612 .5607716
rtvsch | .167237 .0552408 3.03 0.003 .0576408 .2768332
abort | -.6352208 .3266126 -1.94 0.055 -1.283211 .0127692
deathpen | .2753666 .3170247 0.87 0.387 -.3536013 .9043346
_cons | 13.30374 4.282819 3.11 0.002 4.806744 21.80073
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Discuss what happened to views on abortion and its relationship to videogame playing between Models 1, 2, and 3. Why do you think this occurred? Use your knowledge of control variables to advance an explanation.
Note: Question 7 is designed to test your ability to explain these concepts clearly. Spend some time explaining and discussing. A few words likely will not do.
