Question.4788 - SOCI 5314: Social StatisticsAssignment 9Name: _____Juan Garcia ________________Note: Be certain to show all your work including results from SPSS. Points will be deducted if you fail to show your work.1. For which of the following situations would you consider using logistic regression? (8 points) a) To predict a person’s health insurance status (yes or no) from age. b) To predict car mileage from its weight in pounds. c) To examine the relationship between a student’s GPA and his/her support of abortion (favor or oppose). d) To examine the relationship between types of product and customer satisfaction. 2. Briefly define the following terms? (7 points) Risk Ratio : Risk ratio is a measure which compares or predicted the probability of an event occurring in two groups. Odds (Y=1) : The ratio of probability that it will occur [ P ( Y =1 )] to the probability that it will not occur [ P ( Y ≠1 )].Factor : The odds changes when the ith independent variable increases by one unit. 3. Use the GSS2018.sav file, run a logistic regression model to predict a person’s support of death penalty for murder (cappun, favor or oppose death penalty for murder) from his or her political views (POLIVEWS, 1=extremely liberal - 7=extremely conservative). Using appropriate SPSS procedures, answer the following questions: (45 points) Write the prediction equation. P ( Y=1 ) = e-.955+.379x1+e-.955+.379x b) Calculate the predictive probability for someone with an extremely conservative view (=7) and interpret the result. When x = 7 ; P ( Y=1 ) = e-.955+.379(7)1+e-.955+.3797 = e1.6981+e1.698 = 5.461+5.46 = 5.466.46 = 0.845The probability of supporting the death penalty for murder who is extremely conservative ( x =7) is .845, which means that this person is very likely to support the death penalty for a murder. c) Find the risk ratio for a person with an extremely conservative view ( x = 7 ) to a person with an extremely liberal view ( x = 1 ) in terms of their support for death penalty. Interpret the result. When x = 1; P ( Y=1 ) = e-.955+.379(1)1+e-.955+.3791 = e-.5761+e-.576 = .5621+.562 = .5621.562 = 0.360When x = 7 ; P ( Y=1 ) = e-.955+.379(7)1+e-.955+.3797 = e1.6981+e1.698 = 5.461+5.46 = 5.466.46 = 0.845Ratio = 0.8450.360 = 2.45 A person with extremely conservative view is 2.45 times more likely to favor the death penalty than a person with extremely liberal views. d) Using the various measures discussed in class and text, assess the goodness of fit of the model. Does the model fit the data well? (10 points) Classification tables : ( block 0 and block 1 ) Model 0 (No independent variable) has a percentage corrected prediction of 63.2%.Model 1 (including independent variable) has a percentage corrected prediction of 66.8%. Therefore, when we include independent variables, there is a little increase of 3.6%. Histogram of the estimated probability Step number: 1 Observed Groups and Predicted Probabilities 800 + f + I f I I f IF I f IR 600 + f +E I f IQ I f IU I f IE 400 + f +N I f f IC I f f IY I f f O f f I 200 + f f O f f + I O f O f f I I O O O O O O f I I O O O O O O f IPredicted ---------+---------+---------+---------+---------+---------+---------+---------+---------+---------- Prob: 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 Group: OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOffffffffffffffffffffffffffffffffffffffffffffffffff Predicted Probability is of Membership for favor The Cut Value is .50 Symbols: O - Oppose f - favor Each Symbol Represents 50 Cases.Calculate Gm H0 : The independent variable is not important in predicting the dependent variable. HA : The independent variable is important in predicting the dependent variable. From the result, we can observe that significance value ( <.001) is less than 0.05, therefore we accept HA : The independent variable is important in predicting the dependent variable. Hosmer and Lemeshow Test Ho : The model fits the data well. HA : The model does not fit the data well. Since the significance value ( .098 ) is greater than .05, we conclude that we accept H0 : the model fits the data well. Pesudo R – squared: RL2=GmGm+Dm =145.713145.713+2639.949=.052 This is very low; 0 ≤ RL2≤1 PRE measure : Lamda P λp=777-(553+149)777 = 0.097The amount of error increase by 9.7% when the model includes the IV. 0 ≤ λp≤1e) Is the independent variable important in predicting the dependent variable? H0 : β = 0 HA : β ≠0 Since the significance value ( < .001 ) is less than 0.05, we accept HA : β ≠0 f) Calculate the standardized logistic regression coefficient. B* = b * Sx * R / Slogit(Yi) = .379 * 1.50 * .264 / .568 g) Check any violation of assumptions (i.e., normality and outliers). Refit your model to make sure that all assumptions are met. No major violations is observed. Outlier is not a problem. h) Based on results presented by your final model, write an essay about your findings. The essay should include, but not limited to: the effect (strength and direction) of each significant variable on the dependent variable, theoretical implication, and possible limitations of the findings. Using data from the 2018 General Social Survey, this logistic regression analysis determines how political opinions affect support for the death penalty. The findings show a strong, favorable correlation between support for the death penalty and conservatism. In particular, the death sentence for murder is more likely to be supported by conservative people. From extremely liberal to extremely conservative, the probabilities increase by a factor of 2.45, indicating a moderately strong effect. Although the model's predictive value is small (R2 = 0.052), it greatly improves prediction when compared to a model without predictors. This implies that opinions on the death penalty are probably influenced by other, unquantifiable factors, even though political ideology is important.From a theoretical perspective, this finding aligns with traditional conservative ideologies favoring harsher criminal justice policies. However, the limited explanatory power and reliance on self-reported views are key limitations. Future research could benefit from incorporating additional variables such as education, religious beliefs, and personal experience with the justice system to deepen our understanding.4. Select 2 variables from the GSS2018.sav file. Fit the data with a logistic regression model. Justify your selection of these variables. The independent variable should be measured at interval or ratio level. The dependent variable should a dichotomous variable. Use appropriate SPSS procedures, answer the following questions. (40 points): a) Write the prediction equation. I selected ABANY variable as the dependent variable ( Abortion if women wants for any reason ) – Yes or No and POLYVIEWS as the independent variable. P ( Y=1 ) = e-.512+2.079x1+e-.512+2.079xb) Calculate the predictive probability for one case (i.e., select one data value from your independent variable) and interpret the result. When x = 1; P ( Y=1 ) = e-.512+2.079(1)1+e-.512+2.079(1) = e-1.5671+e-1.567 = 4.791+4.79 = 4.795.79 = 0.827 ≈ 0.83The probability of a person supporting the abortion for women if they want with an extremel;y liberal view is 0.83, suggesting that this person is very likely to support the abortion. c) Using the various measures discussed in class and text, assess the goodness of fit of the model. Does the model fit the data well? (10 points) Classification Tables For model 0 without independent variable -percentage correct prediction is 50.8%For model 1 including independent variable – percentage correct prediction is 63.5%.We found that 12.7% increase in the percentage of the correct prediction from model 0 to model 1. Histogram of the estimated probability Step number: 1 Observed Groups and Predicted Probabilities 800 + + I I I IF I IR 600 + Y +E I Y IQ I Y IU I Y IE 400 + Y +N I Y IC I N IY I N I 200 + Y Y N Y + I N Y N Y Y I I N N N Y Y Y I I N N N N N N Y IPredicted ---------+---------+---------+---------+---------+---------+---------+---------+---------+---------- Prob: 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 Group: NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Predicted Probability is of Membership for Yes The Cut Value is .50 Symbols: N - No Y - Yes Each Symbol Represents 50 Cases. Calculate Gm H0 : The independent variable is not important in predicting the dependent variable. HA : The independent variable is important in predicting the dependent variable. From the result, we can observe that significance value ( <.001) is less than 0.05, therefore we accept HA : The independent variable is important in predicting the dependent variable. Hosmer and Lemeshow Test H0 : The model fits the data well. HA : The model does not fit the data well. Since the significance value ( .196 ) is greater than .05, we conclude that we accept H0 : the model fits the data well. Pesudo R – squared: RL2=GmGm+Dm =178.074178.074+1848.358=.088 This is much better as they range from 9 to 15. PRE measure : Lamda P λp=720-(403+131)720 = 0.258 The amount of error increase by 25.8% when the model includes the IV.d) Is the independent variable important in predicting the dependent variable? H0 : β = 0 HA : β ≠0 Since the significance value ( < .001 ) is less than 0.05, we accept HA : β ≠0 e) Calculate the standardized logistic regression coefficient. B* = b * Sx * R / Slogit(Yi) = -5.12 * 1.50 * .342 / .76816 = -0.342 f) Check any violation of assumptions (i.e., normality, outliers, and multicollinearity). Re-specify your model to make sure that all assumptions are met. Outliers is not a problem.g) Based on results presented by your final model, write an essay about your findings. The essay should include, but not limited to: the effect (strength and direction) of each significant variable on the dependent variable, theoretical implication, and possible limitations of the findings.This logistic regression model examined how political views influence support for abortion if a woman wants one for any reason. The results reveal a significant and positive relationship: individuals with more liberal views are substantially more likely to support abortion rights. Specifically, extremely liberal individuals have an 83% predicted probability of support, while support decreases as views become more conservative.From a theoretical perspective, this aligns with known ideological divides—liberal individuals tend to emphasize personal freedom and reproductive rights, whereas conservative ideologies often oppose abortion on moral or religious grounds.The model showed moderate predictive accuracy and good model fit based on the Hosmer and Lemeshow test and PRE-measure. However, the pseudo R-squared value was low, suggesting that other unmeasured variables likely play a role, such as education, religiosity, or personal experiences.Limitations include the assumption of linearity in the logit and the ordinal nature of the POLVIEWS variable, which may not capture nonlinear effects. Future studies could incorporate additional predictors and explore interaction effects to better understand the complexity of abortion attitudes.
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SOCI xxxxxx StatisticsAssignment xxxx Juan xxxxxx Note xx certain xx show xxx your xxxx including xxxxxxx from xxxx Points xxxx be xxxxxxxx if xxx fail xx show xxxx work xxx which xx the xxxxxxxxx situations xxxxx you xxxxxxxx using xxxxxxxx regression xxxxxx a xx predict x person x health xxxxxxxxx status xxx or xx from xxx b xx predict xxx mileage xxxx its xxxxxx in xxxxxx c xx examine xxx relationship xxxxxxx a xxxxxxx s xxx and xxx her xxxxxxx of xxxxxxxx favor xx oppose x To xxxxxxx the xxxxxxxxxxxx between xxxxx of xxxxxxx and xxxxxxxx satisfaction xxxxxxx define xxx following xxxxx points xxxx Ratio xxxx ratio xx a xxxxxxx which xxxxxxxx or xxxxxxxxx the xxxxxxxxxxx of xx event xxxxxxxxx in xxx groups xxxx Y xxx ratio xx probability xxxx it xxxx occur x Y xx the xxxxxxxxxxx that xx will xxx occur x Y xxxxxx The xxxx changes xxxx the xxx independent xxxxxxxx increases xx one xxxx Use xxx GSS xxx file xxx a xxxxxxxx regression xxxxx to xxxxxxx a xxxxxx s xxxxxxx of xxxxx penalty xxx murder xxxxxx favor xx oppose xxxxx penalty xxx murder xxxx his xx her xxxxxxxxx views xxxxxxxx extremely xxxxxxx - xxxxxxxxx conservative xxxxx appropriate xxxx procedures xxxxxx the xxxxxxxxx questions xxxxxx Write xxx prediction xxxxxxxx P x e- x e- x b xxxxxxxxx the xxxxxxxxxx probability xxx someone xxxx an xxxxxxxxx conservative xxxx and xxxxxxxxx the xxxxxx When x P x e- xx e x The xxxxxxxxxxx of xxxxxxxxxx the xxxxx penalty xxx murder xxx is xxxxxxxxx conservative x is xxxxx means xxxx this xxxxxx is xxxx likely xx support xxx death xxxxxxx for x murder x Find xxx risk xxxxx for x person xxxx an xxxxxxxxx conservative xxxx x xx a xxxxxx with xx extremely xxxxxxx view x in xxxxx of xxxxx support xxx death xxxxxxx Interpret xxx result xxxx x x Y xx e- xx e- xxxx x x Y xx e- x e xxxxx A xxxxxx with xxxxxxxxx conservative xxxx is xxxxx more xxxxxx to xxxxx the xxxxx penalty xxxx a xxxxxx with xxxxxxxxx liberal xxxxx d xxxxx the xxxxxxx measures xxxxxxxxx in xxxxx and xxxx assess xxx goodness xx fit xx the xxxxx Does xxx model xxx the xxxx well xxxxxx Classification xxxxxx block xxx block xxxxx No xxxxxxxxxxx variable xxx a xxxxxxxxxx corrected xxxxxxxxxx of xxxxx including xxxxxxxxxxx variable xxx a xxxxxxxxxx corrected xxxxxxxxxx of xxxxxxxxx when xx include xxxxxxxxxxx variables xxxxx is x little xxxxxxxx of xxxxxxxxx of xxx estimated xxxxxxxxxxx Step xxxxxx Observed xxxxxx and xxxxxxxxx Probabilities x I x I x f xx I x IR x E x f xx I x IU x f xx f x I x f xx I x f xx I x f x f x I x f x f x I x f x f x I x O x O x O x f x I x O x O x O x IPredicted xxxxxxxxx --------- xxxxxxxxx --------- xxxxxxxxx --------- xxxxxxxxx --------- xxxxxxxxx ---------- xxxx Group xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Predicted xxxxxxxxxxx is xx Membership xxx favor xxx Cut xxxxx is xxxxxxx O x Oppose x - xxxxx Each xxxxxx Represents xxxxx Calculate xx H xxx independent xxxxxxxx is xxx important xx predicting xxx dependent xxxxxxxx HA xxx independent xxxxxxxx is xxxxxxxxx in xxxxxxxxxx the xxxxxxxxx variable xxxx the xxxxxx we xxx observe xxxx significance xxxxx is xxxx than xxxxxxxxx we xxxxxx HA xxx independent xxxxxxxx is xxxxxxxxx in xxxxxxxxxx the xxxxxxxxx variable xxxxxx and xxxxxxxx Test xx The xxxxx fits xxx data xxxx HA xxx model xxxx not xxx the xxxx well xxxxx the xxxxxxxxxxxx value xx greater xxxx we xxxxxxxx that xx accept x the xxxxx fits xxx data xxxx Pesudo x squared xx GmGm xx This xx very xxx RL xxx measure xxxxx P x - xxx amount xx error xxxxxxxx by xxxx the xxxxx includes xxx IV x e xx the xxxxxxxxxxx variable xxxxxxxxx in xxxxxxxxxx the xxxxxxxxx variable x HA xxxxx the xxxxxxxxxxxx value xx less xxxx we xxxxxx HA x Calculate xxx standardized xxxxxxxx regression xxxxxxxxxxx B x Sx x Slogit xx g xxxxx any xxxxxxxxx of xxxxxxxxxxx i x normality xxx outliers xxxxx your xxxxx to xxxx sure xxxx all xxxxxxxxxxx are xxx No xxxxx violations xx observed xxxxxxx is xxx a xxxxxxx h xxxxx on xxxxxxx presented xx your xxxxx model xxxxx an xxxxx about xxxx findings xxx essay xxxxxx include xxx not xxxxxxx to xxx effect xxxxxxxx and xxxxxxxxx of xxxx significant xxxxxxxx on xxx dependent xxxxxxxx theoretical xxxxxxxxxxx and xxxxxxxx limitations xx the xxxxxxxx Using xxxx from xxx General xxxxxx Survey xxxx logistic xxxxxxxxxx analysis xxxxxxxxxx how xxxxxxxxx opinions xxxxxx support xxx the xxxxx penalty xxx findings xxxx a xxxxxx favorable xxxxxxxxxxx between xxxxxxx for xxx death xxxxxxx and xxxxxxxxxxxx In xxxxxxxxxx the xxxxx sentence xxx murder xx more xxxxxx to xx supported xx conservative xxxxxx From xxxxxxxxx liberal xx extremely xxxxxxxxxxxx the xxxxxxxxxxxxx increase xx a xxxxxx of xxxxxxxxxx a xxxxxxxxxx strong xxxxxx Although xxx model's xxxxxxxxxx value xx small x it xxxxxxx improves xxxxxxxxxx when xxxxxxxx to x model xxxxxxx predictors xxxx implies xxxx opinions xx the xxxxx penalty xxx probably xxxxxxxxxx by xxxxx unquantifiable xxxxxxx even xxxxxx political xxxxxxxx is xxxxxxxxx From x theoretical xxxxxxxxxxx this xxxxxxx aligns xxxx traditional xxxxxxxxxxxx ideologies xxxxxxxx harsher xxxxxxxx justice xxxxxxxx However xxx limited xxxxxxxxxxx power xxx reliance xx self-reported xxxxx are xxx limitations xxxxxx research xxxxx benefit xxxx incorporating xxxxxxxxxx variables xxxx as xxxxxxxxx religious xxxxxxx and xxxxxxxx experience xxxx the xxxxxxx system xx deepen xxx understanding xxxxxx variables xxxx the xxx sav xxxx Fit xxx data xxxx a xxxxxxxx regression xxxxx Justify xxxx selection xx these xxxxxxxxx The xxxxxxxxxxx variable xxxxxx be xxxxxxxx at xxxxxxxx or xxxxx level xxx dependent xxxxxxxx should x dichotomous xxxxxxxx Use xxxxxxxxxxx SPSS xxxxxxxxxx answer xxx following xxxxxxxxx points x Write xxx prediction xxxxxxxx I xxxxxxxx ABANY xxxxxxxx as xxx dependent xxxxxxxx Abortion xx women xxxxx for xxx reason xxx or xx and xxxxxxxxx as xxx independent xxxxxxxx P x e- x e- xx Calculate xxx predictive xxxxxxxxxxx for xxx case x e xxxxxx one xxxx value xxxx your xxxxxxxxxxx variable xxx interpret xxx result xxxx x x Y xx e- xx e- xxx probability xx a xxxxxx supporting xxx abortion xxx women xx they xxxx with xx extremel x liberal xxxx is xxxxxxxxxx that xxxx person xx very xxxxxx to xxxxxxx the xxxxxxxx c xxxxx the xxxxxxx measures xxxxxxxxx in xxxxx and xxxx assess xxx goodness xx fit xx the xxxxx Does xxx model xxx the xxxx well xxxxxx Classification xxxxxx For xxxxx without xxxxxxxxxxx variable xxxxxxxxxxx correct xxxxxxxxxx is xxx model xxxxxxxxx independent xxxxxxxx percentage xxxxxxx prediction xx We xxxxx that xxxxxxxx in xxx percentage xx the xxxxxxx prediction xxxx model xx model xxxxxxxxx of xxx estimated xxxxxxxxxxx Step xxxxxx Observed xxxxxx and xxxxxxxxx Probabilities x I x IF x IR x E x Y xx I x IU x Y xx Y x I x IC x N xx I x I x Y x Y x N x N x Y x I x N x Y x Y x I x N x N x N x IPredicted xxxxxxxxx --------- xxxxxxxxx --------- xxxxxxxxx --------- xxxxxxxxx --------- xxxxxxxxx ---------- xxxx Group xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Predicted xxxxxxxxxxx is xx Membership xxx Yes xxx Cut xxxxx is xxxxxxx N x No x - xxx Each xxxxxx Represents xxxxx Calculate xx H xxx independent xxxxxxxx is xxx important xx predicting xxx dependent xxxxxxxx HA xxx independent xxxxxxxx is xxxxxxxxx in xxxxxxxxxx the xxxxxxxxx variable xxxx the xxxxxx we xxx observe xxxx significance xxxxx is xxxx than xxxxxxxxx we xxxxxx HA xxx independent xxxxxxxx is xxxxxxxxx in xxxxxxxxxx the xxxxxxxxx variable xxxxxx and xxxxxxxx Test x The xxxxx fits xxx data xxxx HA xxx model xxxx not xxx the xxxx well xxxxx the xxxxxxxxxxxx value xx greater xxxx we xxxxxxxx that xx accept x the xxxxx fits xxx data xxxx Pesudo x squared xx GmGm xx This xx much xxxxxx as xxxx range xxxx to xxx measure xxxxx P x - xxx amount xx error xxxxxxxx by xxxx the xxxxx includes xxx IV x Is xxx independent xxxxxxxx important xx predicting xxx dependent xxxxxxxx H xx Since xxx significance xxxxx is xxxx than xx accept xx e xxxxxxxxx the xxxxxxxxxxxx logistic xxxxxxxxxx coefficient x b xx R xxxxxx Yi x - x Check xxx violation xx assumptions x e xxxxxxxxx outliers xxx multicollinearity xxxxxxxxxx your xxxxx to xxxx sure xxxx all xxxxxxxxxxx are xxx Outliers xx not x problem x Based xx results xxxxxxxxx by xxxx final xxxxx write xx essay xxxxx your xxxxxxxx The xxxxx should xxxxxxx but xxx limited xx the xxxxxx strength xxx direction xx each xxxxxxxxxxx variable xx the xxxxxxxxx variable xxxxxxxxxxx implication xxx possible xxxxxxxxxxx of xxx findings xxxx logistic xxxxxxxxxx model xxxxxxxx how xxxxxxxxx views xxxxxxxxx support xxx abortion xx a xxxxx wants xxx for xxx reason xxx results xxxxxx a xxxxxxxxxxx and xxxxxxxx relationship xxxxxxxxxxx with xxxx liberal xxxxx are xxxxxxxxxxxxx more xxxxxx to xxxxxxx abortion xxxxxx Specifically xxxxxxxxx liberal xxxxxxxxxxx have xx predicted xxxxxxxxxxx of xxxxxxx while xxxxxxx decreases xx views xxxxxx more xxxxxxxxxxxx From x theoretical xxxxxxxxxxx this xxxxxx with xxxxx ideological xxxxxxx liberal xxxxxxxxxxx tend xx emphasize xxxxxxxx freedom xxx reproductive xxxxxx whereas xxxxxxxxxxxx ideologies xxxxx oppose xxxxxxxx on xxxxx or xxxxxxxxx grounds xxx model xxxxxx moderate xxxxxxxxxx accuracy xxx good xxxxx fit xxxxx on xxx Hosmer xxx Lemeshow xxxx and xxxxxxxxxxx However xxx pseudo xxxxxxxxx value xxx low xxxxxxxxxx that xxxxx unmeasured xxxxxxxxx likely xxxx a xxxx such xx education xxxxxxxxxxx or xxxxxxxx experiences xxxxxxxxxxx include xxx assumption xx linearity xx the xxxxx and xxx ordinal xxxxxx of xxx POLVIEWS xxxxxxxx which xxx not xxxxxxx nonlinear xxxxxxx Future xxxxxxx could xxxxxxxxxxx additional xxxxxxxxxx and xxxxxxx interaction xxxxxxx to xxxxxx understand xxx complexity xx abortion xxxxxxxxxMore Articles From Social Statistics
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