Texas State University



.Texas State UniversitySchool of Criminal JusticePh.D. Comprehensive Exam for StatisticsOctober 11, 20169:00 a.m. – 11:00 a.m.DIRECTIONS: Choose Option One or Option Two.Save two electronic copies of your answer (one with your ID number assigned to you, the other with your ID number and name). Email both copies to Cybele Hinson ch56@txstate.edu. Print out and turn in a hard copy as well with both your ID number and name on it.Option 1:Background and MotivationThis exam centers on the relationship between self-control, age, and violence. Although inconsistent with the notion that one’s level of self-control is invariant, this exam states that age moderates the relationship between self-control and engaging in violence. This exam relies on the data from a sample of adolescent respondents. Estimate a multivariate ordinary least squares regression model to test the following hypothesis: The effect of self-control on engaging in violence decreases as age increases. You may use a calculator. You will be assessed based on your responses to the following items:1.Using the data file described below, use SPSS to estimate a multivariate ordinary least squares regression equation. The dependent variable is a continuous measure of engaging in violent behavior. The primary independent variables are: (1) a continuous, mean-centered measure of self-control (where higher values indicate more self-control); (2) a continuous, mean-centered measure of age in years; and (3) the mathematical product of these two variables allowing for a statistical interaction between them.Hold constant the potentially confounding effects of the respondent’s: (1) family attachment; (2) sex; (3) employment status; and (4) membership in an academic honor society.2.Explain and discuss the model fit statistics for the model that you estimated. Explain also the quantities used for the F value.3.Based on the model you estimated, and while being mindful of the ways in which variable values are expressed, interpret and discuss (a) the y-intercept; (b) the slopes (i.e., the partial regression coefficients) for the primary independent variables; (c) the slope for academic honor society membership; and (d) these quantities' tests of statistical significance.4.Explain whether and how these results support the motivating hypothesis.5.The standard deviation of age is 1.94. When age is one standard deviation above the mean, what is the effect of self-control on violence? Report the actual numeric value.6.Diagnose the estimated model with regard to outlying and non-outlying influence. Discuss the evidence that is relevant to whether observations are considered influential. If evidence for problems exists, do not address problems with additional analysis.7. Other than collinearity, explain and discuss (a) the model’s assumptions; and (b) the desirable properties that OLS estimates have when their assumptions are metThe data file contains data from 500 individual respondents. The variables relevant to the exam are named and described below.Data File Contents for ExamVariable NameVariable Descriptionviol =A continuous measure for the respondent’s frequency of engaging in violent behavior. Higher values indicate more violence. Refer to units of this variable as points on the violent-behavior scale.selfcon=A continuous and mean-centered measure of the respondent’s self-control level. Higher values indicate a higher self-control level. Refer to units of this variable as points on the self-control scale.age =A continuous and mean-centered measure of the respondent’s age in years. Higher values indicate higher age. Refer to units of this variable as age in years.product The product-term for the statistical interaction between self-control and age (that is, product = selfcon × age).family =A continuous measure of the respondent’s level of attachment to their family. Higher values indicate more family attachment. Refer to units of this variable as units on the family-attachment scale.male A dummy-coded variable measuring whether the respondent is male.0 = No1 = Yesemploy =A dummy-coded variable measuring whether the respondent is employed (that is, has a job).0 = No1 = Yeshonor =A dummy-coded variable measuring whether the respondent is a member of an academic honor society.0 = No1 = YesEnd of Option 1Option 2:Background and MotivationThis exam centers on the relationship between self-control, age, and violence. Although inconsistent with the notion that one’s level of self-control is invariant, this exam states that age moderates the relationship between self-control and engaging in violence.This exam relies on the data from a sample of adolescent respondents. Estimate a multivariate ordinary least squares regression model to test the following hypothesis: The effect of self-control on engaging in violence decreases as age increases.The investigator used a multivariate ordinary least squares (OLS) regression model to test this hypothesis. The dependent variable is a continuous measure of self-reported violence. The results of the estimation are presented in the table below.You may use a calculator. You will be assessed based on your responses to the following items:1. Based on the results, explain and discuss the F test and the model fit statistics. 2.Based on the results and while being mindful of the ways in which the variable values are expressed, interpret (a) the constant (that is, the y-intercept); (b) the coefficient for self-control; (c) the coefficient for age; and (d) the coefficient for the product term (that is, self-control × age).3.(a) Age has a standard deviation of 1.75 in this sample. Based on the results, what is the effect of self-control on violence when age is one standard deviation above its mean level?A. -0.476B. -0.318C. -0.686D. 0.210E. 1.074(b) Given this level of age (that is, an age of 1.75 standard deviations above the mean age), what is the t value for the effect of self-control on violence? Assume the standard error for the effect of self-control on violence is constant across values of age. Report the actual numerical value. Is this effect statistically significant at the .05 level of statistical significance? (c) Explain whether and how these results support the motivating hypothesis.4.Based on the results, report the numeric value for the residual variance and the numeric value for the residual sum of squares.5. Other than collinearity, explain and discuss (a) the model’s assumptions; (b) how these assumptions are evaluated; and (c) how violations to assumptions are defined, detected and addressed.Table for statistics exam, option 2Ordinary least squares model explaining violenceN = 1,621VariablesEffectSEpVIFSelf-Controla-0.6860.056< .0011.16Agea1.0740.229< .0011.26Self-Controla × Agea0.2100.604.0011.32Maleb0.3320.106.0021.03Whiteb-0.0010.002.6731.01Academic Honorsb-0.5800.133< .0011.02Religiosity-0.0060.028.8191.10Constant3.8690.515< .001--Model-fit statisticsR2=0.1418 Root MSE=2.117Fdf1=7, df2=1613,=38.07a A continuous variable that is centered on its mean.b A dummy-coded variable where zero indicates absence of characteristic.End of Option 2 ................
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