Stat252FinalPracticeQuestionsLarge_Winter2020

Stat 252 – Final Exam Practice Questions – Mike Kowalski 3 2. Do the effects of gender depend on class? Tests of Between-Subjects Effects Dependent Variable: VERBAL 5843.036 a 7 834.719 16.351 .000 81121.953 1 81121.953 1589.060 .000 5513.139 3 1837.713 35.998 .000 57.291 1 57.291 1.122 .293 272.605 3 90.868 1.780 .159 3675.621 72 51.050 90640.610 80 9518.657 79 Source Corrected Model Intercept CLASS GENDER CLASS * GENDER Error Total Corrected Total Type III Sum of Squares df Mean Square F Sig. R Squared = .614 (Adjusted R Squared = .576) a.

Stat 252 – Final Exam Practice Questions – Mike Kowalski 6 5. Consider the following model effect: The overall additive effect of class 1 vs. class 2. Define and estimate this effects using a linear combination of means. Descriptive Statistics Dependent Variable: VERBAL 25.7800 8.57319 10 19.5400 5.74344 10 22.6600 7.79024 20 29.9500 7.88730 10 28.3100 6.28056 10 29.1300 6.99000 20 28.2700 8.48555 10 32.2700 4.21638 10 30.2700 6.83660 20 46.7600 8.85490 10 43.8700 5.66295 10 45.3150 7.38443 20 32.6900 11.66045 40 30.9975 10.32633 40 31.8438 10.97676 80 GENDER f m Total f m Total f m Total f m Total f m Total CLASS 1.00 2.00 3.00 4.00 Total Mean Std. Deviation N

Stat 252 – Final Exam Practice Questions – Mike Kowalski 9 2. Has homework got you depressed? It could be worse. Depression, like other illness, is more prevalent among adults with less education than you have. Suppose a study was done to investigate the association of depression with age, education level and gender. A survey of 18 adults aged 18 to 90 was done. They modeled a depression score from responses to several related questions. Education was categorized as (i) college degree ( cd ), (ii) high school diploma plus some college ( hiplus ), (iii) high school diploma only ( hionly ). As well, gender was simply categorized as (i) male, (ii) female. Age is modeled as continuous variables. To fit a MLR model, the indicator variables cd, hiplus and female are used to indicate the level of their respective categorical variables. Use the following model to answer the questions. 0 1 2 3 4 5 6 7 8 9 10 11 { | , , } ( ) ( ) ( ) ( ) ( ) ( ) ( ) score age EDUC GEN age cd hiplus fem age cd age hiplus age fem cd fem hiplus fem age cd fem age hiplus fem                                   a) In terms of the coefficients , what is the effect of age on mean depression score for each combination of education and gender?

Stat 252 – Final Exam Practice Questions – Mike Kowalski 12 c) Does the effect of age on mean score differ in any way between the education/gender groups? Education Gender Effect of age on mean score cd male 1 5    hiplus male 1 6    hionly male 1  cd female 1 5 7 10        hiplus female 1 6 7 11        hionly female 1 7   

Stat 252 – Final Exam Practice Questions – Mike Kowalski 15 f) Modify the model to specify that the effect of age on mean score is possibly different between males and females only when they have high school only, otherwise the effects of age are the same for males and females with the same education level. Education Gender Effect of age on mean score cd male 1 5    hiplus male 1 6    hionly male 1  cd female 1 5 7 10        hiplus female 1 6 7 11        hionly female 1 7   

Stat 252 – Final Exam Practice Questions – Mike Kowalski 18 Regression Output for Model 1: Explanatory Variables – age, EDUCATION and their interaction. ANOVA b 128.616 5 25.723 16.690 .000 a 18.495 12 1.541 147.111 17 Regression Residual Total Model 1 Sum of Squares df Mean Square F Sig. Predictors: (Constant), agehiplus, age, agecd, cd, hiplus a. Dependent Variable: score b. Coefficients a -8.667 2.767 -3.132 .009 .467 .099 .847 4.717 .000 1.190 3.779 .196 .315 .758 -1.229 3.845 -.203 -.319 .755 .010 .140 .041 .068 .947 .114 .140 .513 .817 .430 (Constant) age cd hiplus agecd agehiplus Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: score a.

Stat 252 – Final Exam Practice Questions – Mike Kowalski 21 j) Suppose it is discovered that gender has no effect on mean depression score. Also, suppose the effect of age is the same for all levels of education. In the resulting model, carry out a test to determine if the lines for individuals with college degree and those with high school only are any different. Set up the null and alternative hypotheses, calculate the test statistic, state its null distribution, approximate the p-value and state your conclusion in plain English. ANOVA b 127.349 3 42.450 30.073 .000 a 19.762 14 1.412 147.111 17 Regression Residual Total Model 1 Sum of Squares df Mean Square F Sig. Predictors: (Constant), hiplus, age, cd a. Dependent Variable: score b. Coefficients a -9.802 1.579 -6.206 .000 .508 .055 .922 9.293 .000 1.516 .695 .250 2.182 .047 1.841 .688 .304 2.676 .018 (Constant) age cd hiplus Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: score a.

Stat 252 – Final Exam Practice Questions – Mike Kowalski 22 k) In model 2 (as defined in the output), compute an approximate 95% prediction interval for the depression score of a 25 year old individual with a college degree. ANOVA b 127.349 3 42.450 30.073 .000 a 19.762 14 1.412 147.111 17 Regression Residual Total Model 1 Sum of Squares df Mean Square F Sig. Predictors: (Constant), hiplus, age, cd a. Dependent Variable: score b. Coefficients a -9.802 1.579 -6.206 .000 .508 .055 .922 9.293 .000 1.516 .695 .250 2.182 .047 1.841 .688 .304 2.676 .018 (Constant) age cd hiplus Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: score a.

Stat 252 – Final Exam Practice Questions – Mike Kowalski 23 l) Estimate the additive effect of age on mean score. Do this using both Models 1 and 2. Compare. Coefficients a -8.667 2.767 -3.132 .009 .467 .099 .847 4.717 .000 1.190 3.779 .196 .315 .758 -1.229 3.845 -.203 -.319 .755 .010 .140 .041 .068 .947 .114 .140 .513 .817 .430 (Constant) age cd hiplus agecd agehiplus Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: score a. Coefficients a -9.802 1.579 -6.206 .000 .508 .055 .922 9.293 .000 1.516 .695 .250 2.182 .047 1.841 .688 .304 2.676 .018 (Constant) age cd hiplus Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: score a.

Stat 252 – Final Exam Practice Questions – Mike Kowalski 24 m) Suppose you removed ‘age’ from Model 2. What are the SSR and df for the reduced model? Coefficients a -9.802 1.579 -6.206 .000 .508 .055 .922 9.293 .000 1.516 .695 .250 2.182 .047 1.841 .688 .304 2.676 .018 (Constant) age cd hiplus Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: score a.