# The smallest number of regression models

1.) The smallest number of regression models you need to have nested modeling is:a.) 1b.) 2c.) 3d.) 42.) What statistical test do we use to see if a second regression model is better than the first regression model?a.) the chi-square testb.) the t-testc.) the improvement testd.) the F-test3.) Here are two models made from using GSS2006 data. The dependent variable is hours of television watched per day:Independent Variable Model 1 Model 2Age (in years) 0.02*** 0.00Working or Retired — 1.32***Constant 1.70 2.51R-Squared 0.03 0.06n 1523 1523Which of the following pairs of people watches the same hours of television?a.) a retired 50-year-old and a retired 80-year-oldb.) two 80 year-olds: one who is working, one who is retiredc.) two 50-year-olds: one who is working, one who is retiredd.) a 20-year-old working person and an 86-year-old retired person4.) 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 religious up to 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 2Age (in years) 0.03*** 0.03***Sex (, ) — -0.93***Constant 4.23 4.65R-Squared 0.04 0.07n 2912 2912Which 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 2Education (in years) 0.35*** ???Income (in thousands of dollars) — 0.03***Constant 0.50 -2.50R-Squared 0.10 0.15n 1000 1000To support the hypothesis, what is the most likely number that would go in the place of the “???” in Model 2?a.) .03b.) .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 relationshipb.) a dependent relationshipc.) an independent relationshipd.) a controlling relationship7.)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—————————————————————————— 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——————————————————————————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—————————————————————————— 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——————————————————————————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—————————————————————————— 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——————————————————————————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.