Name: Directions : For Section One you will be asked to respond to a set of multiple choice items and a few short answer items. The second section you will use three SPSS outputs to answer the homework questions. These outputs are provided to you and will just need to be printed out. NOTE: Some values (e.g., degrees of freedom, significance levels) have been intentionally deleted from the output and will need to be computed to answer the homework questions. To assist in understanding the meaning and metric of the variables there is a variable definition sheet that also must be printed out. Be sure to write your name on all pieces of paper and turn everything back in (i.e., agreement form, homework and all output). SECTION ONE - Choose the best answer for each multiple choice question. Then, provide a one paragraph justification or an illustrative example for why your selected answer is the correct one. (Each multiple choice item is worth 2 points) 1. The Y-intercept is the value of a person’s predicted score when X equals: a. 1.0 b. 0.0 c. mean of Y d. mean of X Justification: 2. The Y-intercept of a regression line is: a. the value of X at the point where the regression line crosses the X-axis. b. the value of X at the point where the regression line crosses the Y-axis. c. the value of Y at the point where the regression line crosses the X-axis. d. the value of Y at the point where the regression line crosses the Y-axis. Justification: 3. In general, the greater the proportion of variance accounted for: a. the more error there is in the data. b. the less accurately we can predict or explain behavior. c. the more accurately we can predict or explain behavior. d. the less important the relationship to our ability to make predictions. Name: Justification: 4. In general, as independent variables are added to a regression model, the unstandardized regression coefficients previously entered are expected to: a. become smaller in value or magnitude. b. become larger in value or magnitude. c. remain the same value regardless of the number of independent variables. d. approach the value of the zero order correlation coefficient. Justification: 5. The coefficient of determination is interpreted as: a. the amount of variance explained in all of the independent variable scores. b. the degree to which the dependent variable scores are reliable. c. the proportion of variance in the dependent variable scores that has been accounted for . d. the proportion of variance in the dependent variable scores that has not been accounted for. Justification: 6. In order to have a high multiple correlation (R) or a high R squared value, a researcher would want independent variables that correlate _______ with the dependent variable and correlate _______ with each other. a. low, low b. low, high c. high, low d. high, high Justification: 7. For a set of paired (X,Y) values the Sum of Squares Total is equal to 40 and the zero order correlation coefficient (Pearson correlation coefficient) between X and Y is .60. What is the value of the Sum of Squares Regression? a. b. c. .36 .60 14.4 2 Name: d. 24.0 Justification: 8. Imagine a set of data where the zero order correlation between Y (the dependent variable) and X1 (the first independent variable) = .10, the zero order correlation between Y (the dependent variable) and X2 (the second independent variable) = .70 and the zero order correlation between Y (the dependent variable) and X3 (the third independent variable) = -.20. For the same data set assume that the zero order correlation between X1 and X2 =0; the zero order correlation between X1 and X3 =0 and the zero order correlation between X2 and X3 =0, then what would be the value of R2? Demonstrate and explain how you determined your answer. If you do not show your work, no points will be awarded. (2 pts) 9. A panel of educators in a large urban community wanted to evaluate the effects of educational resources on student performance. They examined the relationship between 12th grade mean verbal SAT scores (Y) and the following independent variables for a random sample of 25 high schools: X1 3 Name: = Per pupil expenditure in dollars; X2 = Percentage of teachers with a master’s degree or higher; and X3 = Pupil to teacher ratio. The following sum of squares values can be used to summarize the key results from using the three independent variables to explain the variability in the SAT scores. Sum of Squares Total = 28522.24 Sum of Squares Residual = 20391.75 a. Using any SPSS Linear Regression output as a guide, construct an ANOVA table from the Model Summary section when X1, X2, and X3 are used to explain the variability in Y. (You do not need to include the Sig column since you do not have access to the exact probability value.) (4 pts) b. What is the value of the R2 for the model in part 9a? When using an alpha level of .05, is this value significantly different than zero? Justify your answer. This includes providing the parameter being estimated, the statistical test (F, t, etc.) and its value, degrees of freedom associated with the statistical test, and the critical F value associated with this test. (4 pts) c. Based on the R2 value in part b and your statistical decision, comment on whether the linear composite of educational resources (the regression equation using your IVs) appears to be associated with student performance. (1 pt) SECTION TWO: For this portion of the exam use the SPSS outputs provided or a critical value F or t table to answer the following questions. You will have to decide which of the outputs that are provided to you best answer each specific question. Remember a variable definition sheet is attached to this exam to aid in interpretation of the variables. 4 Name: 10. 11. Among the six independent variables provided, which one would account for or explain the greatest amount of variance in the STRESS variable if it were the only independent variable you were allowed to use in a regression model? In other words, you could only conduct a bivariate linear regression as opposed to a multiple linear regression. Calculate the proportion of variance this variable would account for in the STRESS scores (the dependent variable). (4 pts) Using the unstandardized regression coefficient and an alpha level of .05, interpret the correlation (including the direction) between traditionality toward childrearing (TRAD) and the mother’s reported level of stress with her child (STRESS) after controlling for locus of control (LOCNTRL) and the reported quality of the relationship the mother has with her partner or spouse (RELAT). In order to receive full credit you must interpret the correlation in the context of the variable using the definition sheet. It is not acceptable to just say the correlation is positive or the correlation is negative. Indicate the basis for your conclusion by identifying the value of the test statistics (F, t, etc.), the degrees of freedom, and your statistical decision. (5 pts) 12. Identify and name the type of parameter (e.g., squared semi-partial correlation coefficient) that is being estimated along with the values from your set of outputs for each of the following: (10 pts) Hint: You will need to find the output that contains the model with only the independent variable of interest for each question. Also, remember there is a difference between r, r2, and R2 values. a. r STRESS (RELAT∙ TRAD, LCONTROL) b. r STRESS, LOCNTROL ∙ M_AGE, INCOME, GENDER, TRAD c. R2 STRESS ∙ INCOME, GENDER, M_AGE d. r2 STRESS, M_AGE ∙INCOME, GENDER e. R2 STRESS ∙ M_AGE, INCOME, GENDER, LOCNTROL, TRAD 13. Use the SPSS output from the full model containing all six independent variables to respond to the following set of questions. 5 Name: a. What is the total proportion of STRESS variance accounted for by the full six independent variable model? (2 pts) b. Does the proportion in part a) represent a statistically significant amount of variance in the STRESS scores? Indicate the basis for your conclusion by identifying the value of the test statistics (F, t, etc.) the degrees of freedom, the critical value and/or the observed significance level used in making the statistical decision. (4 pts) c. Do any of the six individual variables contribute a statistically significant proportion of unique variance (using an alpha level of .05) in the STRESS scores? Answer yes or no for each of the six variables. For those that you have answered yes, what is the unique variance associated with these variables? Indicate the basis for your conclusion by identifying the values of the parameter being estimated, the test statistics (F, t, etc.) the degrees of freedom, the critical value and/or the observed significance level used in making the statistical decisions. (16 pts) 6 Name: 14. Using the appropriate unstandardized regression equation, what is the predicted STRESS score for a mother whose observed scores on the independent variables are as follows: (3 pts) It is important to show all of your work for full credit. M_AGE = 30 INCOME = $42,800 GENDER = girl (X value would be coded as a 1) LOCNTROL = 45 TRAD = 54 RELAT = 2 15. Use the SPSS outputs to assist in answering the following questions regarding variables entered as a set of variables versus variables entered into a model one individual variable at a time. a. What is the unique contribution of the set of variables TRAD and LOCNTRL in the STRESS scores over and above (or after accounting for) the three family demographic variables (M_AGE, INCOME and GENDER)? Indicate the basis for your conclusion by identifying the value(s) of the parameter being estimated, the test statistic(s) (F, t, etc.) the degrees of freedom, the critical value(s) and/or the observed significance level(s) used in making the statistical decision(s) (3 pts) b. Would you expect M_AGE, INCOME, and GENDER taken as a set to contribute a significant amount of unique variance to the STRESS scores in a model already containing LOCNTROL, TRAD, and RELAT? (NOTE: You do not have an output directly matching this question. You should be able to make an educated guess based on the output that you do have.) Indicate the basis and rationale for your decision. (2 pts) 7 GET FILE='C:\EPSY 810\Fall2017\EPSY 810 Exam data.sav'. DATASET NAME DataSet1 WINDOW=FRONT. REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA CHANGE ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT stress /METHOD=ENTER income m_age /METHOD=ENTER gender /METHOD=ENTER locntrl trad /METHOD=ENTER relat . Regression [DataSet1] 'C:\EPSY 810\Fall2017\EPSY 810 Exam data.sav' Descriptive Statistics stress income m_age gender locntrl trad relat Mean 63.0208 30767.54 28.2632 .5000 47.9561 58.1754 3.8991 Std. Dev iat ion 12.63602 19428.01324 5.66006 .50221 7.39815 14.73257 .77910 N 114 114 114 114 114 114 114 Correlations Pearson Correlation Sig. (1-tailed) N stress 1.000 -.188 -.027 -.052 .465 .295 -.271 . .022 .389 .292 .000 .001 .002 114 114 114 114 114 114 114 stress income m_age gender locntrl trad relat stress income m_age gender locntrl trad relat stress income m_age gender locntrl trad relat income -.188 1.000 .497 -.146 -.074 -.285 .175 .022 . .000 .060 .217 .001 .031 114 114 114 114 114 114 114 m_age -.027 .497 1.000 .053 .149 -.330 .029 .389 .000 . .288 .056 .000 .378 114 114 114 114 114 114 114 gender -.052 -.146 .053 1.000 .042 -.047 -.089 .292 .060 .288 . .330 .311 .174 114 114 114 114 114 114 114 locntrl .465 -.074 .149 .042 1.000 .078 -.130 .000 .217 .056 .330 . .206 .084 114 114 114 114 114 114 114 trad .295 -.285 -.330 -.047 .078 1.000 -.250 .001 .001 .000 .311 .206 . .004 114 114 114 114 114 114 114 relat -.271 .175 .029 -.089 -.130 -.250 1.000 .002 .031 .378 .174 .084 .004 . 114 114 114 114 114 114 114 Variabl es Entered/Removedb Model 1 2 3 4 Variables Entered m_age, a income gender a locntrl, trada relat a Variables Remov ed Method . Enter . . . Enter Enter Enter a. All requested v ariables entered. b. Dependent Variable: stress 2 Model Summary Change Statistics Model 1 2 3 R R Square .203a .223b .050 c 4 d Adjusted R Square .024 .024 Std. Error of the Est imat e 12.48300 12.48350 R Square Change .041 .009 F Change 2.394 .991 .266 10.82757 .248 19.109 .282 10.70352 .022 3.518 df 1 2 1 df 2 111 110 Sig. F Change .096 .322 1 107 .063 a. Predictors: (Const ant ), m_age, income b. Predictors: (Const ant ), m_age, income, gender c. Predictors: (Const ant ), m_age, income, gender, locntrl, t rad d. Predictors: (Const ant ), m_age, income, gender, locntrl, t rad, relat ANOVAe Model 1 2 3 4 Regression Residual Total Regression Residual Total Regression Residual Total Regression Residual Total Sum of Squares 745.983 17296.608 18042.591 900.433 17142.158 18042.591 5381.065 12661.526 18042.591 df 2 111 113 3 110 113 5 108 113 Mean Square 372.992 155.825 F 2.394 Sig. .096a 300.144 155.838 1.926 .130b 1076.213 117.236 9.180 .000c 964.017 8.415 5784.101 12258.490 18042.591 d 114.565 113 a. Predictors: (Constant), m_age, income b. Predictors: (Constant), m_age, income, gender c. Predictors: (Constant), m_age, income, gender, locntrl, trad d. Predictors: (Constant), m_age, income, gender, locntrl, trad, relat e. Dependent Variable: stress 3 Coeffici entsa Model 1 2 3 4 (Constant) income m_age (Constant) income m_age gender (Constant) income m_age gender locntrl trad (Constant) income m_age gender locntrl trad relat Unstandardized Coef f icients B Std. Error 62.062 6.102 .000 .000 .198 .239 62.690 6.134 .000 .000 .234 .242 -2.379 2.390 15.706 9.537 .0000 .000 .124 .221 -2.017 2.077 .737 .142 .206 .075 29.340 11.904 .000 .000 .087 .219 -2.294 2.058 .715 .141 .174 .076 -2.554 1.361 Standardized Coef f icients Beta -.232 .089 -.254 .105 -.095 -.127 .056 -.080 .432 .240 -.105 .039 -.091 .419 .202 -.157 t 10.171 -2.169 .830 10.219 -2.324 .967 -.996 1.647 -1.308 .562 -.971 5.182 2.760 2.465 -1.081 .398 -1.115 5.068 2.290 -1.876 Sig. .000 .032 .408 .000 .022 .336 .322 .102 .194 .575 .334 .000 .007 .015 .282 .691 .267 .000 .024 .063 Correlations Zero-order Part ial Part -.188 -.027 -.202 .079 -.202 .077 -.188 -.027 -.052 -.216 .092 -.094 -.216 .090 -.093 -.188 -.027 -.052 .465 .295 -.125 .054 -.093 .446 .257 -.105 .045 -.078 .418 .222 -.188 -.027 -.052 .465 .295 -.271 -.104 .038 -.107 .440 .216 -.178 -.086 .032 -.089 .404 .182 -.149 a. Dependent Variable: stress Excluded Variablesd Model 1 2 3 gender locntrl trad relat locntrl trad relat relat Beta In -.095a .458a .297a -.242a .458b .292b -.248b -.157c t -.996 5.366 3.093 -2.623 5.371 3.031 -2.688 -1.876 Sig. .322 .000 .003 .010 .000 .003 .008 .063 Part ial Correlation -.094 .455 .283 -.243 .457 .279 -.249 -.178 Collinearity Stat istics Tolerance .958 .948 .872 .965 .948 .868 .962 .901 a. Predictors in t he Model: (Constant), m_age, income b. Predictors in t he Model: (Constant), m_age, income, gender c. Predictors in t he Model: (Constant), m_age, income, gender, locntrl, trad d. Dependent Variable: stress 4 REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA CHANGE ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT stress /METHOD=ENTER relat locntrl trad. Regression [DataSet1] 'C:\EPSY 810\Fall2017\EPSY 810 Exam data.sav' Descriptive Statistics stress relat locntrl trad Mean 63.0208 3.8991 47.9561 58.1754 Std. Dev iat ion 12.63602 .77910 7.39815 14.73257 N 114 114 114 114 Correlations Pearson Correlation Sig. (1-tailed) N stress 1.000 -.271 .465 .295 . .002 .000 .001 114 114 114 114 stress relat locntrl trad stress relat locntrl trad stress relat locntrl trad relat -.271 1.000 -.130 -.250 .002 . .084 .004 114 114 114 114 locntrl .465 -.130 1.000 .078 .000 .084 . .206 114 114 114 114 trad .295 -.250 .078 1.000 .001 .004 .206 . 114 114 114 114 Variables Entered/Removedb Model 1 Variables Entered trad, locntrl, a relat Variables Remov ed . Method Enter a. All requested v ariables entered. b. Dependent Variable: stress 5 Model Summary Change Statistics Model 1 R R Square .555a .308 Adjusted R Square .289 Std. Error of the Est imat e 10.65722 R Square Change .308 F Change 16.286 df 1 3 df 2 110 Sig. F Change .000 a. Predictors: (Const ant ), trad, locntrl, relat ANOVAb Model 1 Regression Residual Total Sum of Squares 5549.190 12493.402 18042.591 df 3 110 113 Mean Square 1849.730 113.576 F 16.286 Sig. .000a a. Predictors: (Constant), trad, locntrl, relat b. Dependent Variable: stress Coeffi ci entsa Model 1 (Constant) relat locntrl trad Unstandardized Coef f icients B St d. Error 27.140 10.181 -2.605 1.338 .729 .137 .191 .070 St andar dized Coef f ici ents Beta -.161 .427 .222 t 2.666 -1.947 5.327 2.709 Sig. .009 .054 .000 .008 Correlations Zero-order Part ial -.271 .465 .295 -.183 .453 .250 Part -.155 .423 .215 a. Dependent Variable: stress 6 REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA CHANGE ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT stress /METHOD=ENTER gender income m_age . Regression [DataSet1] 'C:\EPSY 810\Fall2017\EPSY 810 Exam data.sav' Descriptive Statistics stress gender income m_age Mean 63.0208 .5000 30767.54 28.2632 Std. Dev iat ion 12.63602 .50221 19428.01324 5.66006 N 114 114 114 114 Correlati ons Pearson Correlation Sig. (1-tailed) N stress 1.000 -.052 -.188 -.027 . .292 .022 .389 114 114 114 114 stress gender income m_age stress gender income m_age stress gender income m_age gender -.052 1.000 -.146 .053 .292 . .060 .288 114 114 114 114 income -.188 -.146 1.000 .497 .022 .060 . .000 114 114 114 114 m_age -.027 .053 .497 1.000 .389 .288 .000 . 114 114 114 114 Variabl es Entered/Removedb Model 1 Variables Entered m_age, gender, a income Variables Remov ed . Method Enter a. All requested v ariables entered. b. Dependent Variable: stress 7 Model Summary Change Statistics Model 1 R R Square .223a .050 Adjusted R Square .024 Std. Error of the Est imat e 12.48350 R Square Change .050 F Change 1.926 df 1 3 df 2 110 Sig. F Change .130 a. Predictors: (Const ant ), m_age, gender, income ANOVAb Model 1 Regression Residual Total Sum of Squares 900.433 17142.158 18042.591 df 3 110 113 Mean Square 300.144 155.838 F 1.926 Sig. .130a a. Predictors: (Constant), m_age, gender, income b. Dependent Variable: stress Coeffici entsa Model 1 (Constant) gender income m_age Unstandardized Coef f icients B Std. Error 62.690 6.134 -2.379 2.390 .000 .000 .234 .242 Standardized Coef f icients Beta -.095 -.254 .105 t 10.219 -.996 -2.324 .967 Sig. .000 .322 .022 .336 Correlations Zero-order Part ial -.052 -.188 -.027 -.094 -.216 .092 Part -.093 -.216 .090 a. Dependent Variable: stress 8 EPSY 810 Fall 2017 Exam Section 2 Variable Definitions STRESS = Abidin Parenting Stress Index - This variable represents the level of day-to-day stress reported by mothers when they are raising a young child. Higher scores represent higher stress; lower scores represent lower levels of reported stress. Scores can range from 30 to 150. M_AGE = mother’s age in years INCOME = total family income per year GENDER = child gender (when X = 0 the child is a boy; when X = 1 the child is girl) LOCNTRL = Locus of control -This variable represents parental beliefs of having control over their baby’s behavior. The scale contains 20 items on a 5-point Likert scale; scores can vary from 20 to 100. High scores represent parental beliefs that the baby is in control over the parents’ lives; low scores represent parental control over their own lives. TRAD = Traditional ideas toward childrearing -This variable represents parental ideas toward childrearing with high scores meaning more traditional feelings toward childrearing and low scores representing more progressive or modern beliefs. Scores can range from 22 to 110. RELAT – Relationship with partner or spouse -This variable represents the reported quality of the relationship the mother has with her partner or spouse. High scores represent the mother’s feelings of a high quality relationship; low scores represent the mother’s feelings of a lack of quality. Scores can range from 1 to 7.
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