1 Psych 541 Online Test 3 Summer 2017 59 points 1. (14 points) A researcher wanted to examine the degree to which IQ and Study Time (hours per week) predict grade point average. The data are presented below along with the results of a simultaneous multiple regression (backwards and interpret model 1). Please answer the following questions about the output. IQ 110.0 112.0 118.0 119.0 122.0 125.0 127.0 130.0 132.0 134.0 136.0 138.0 Study 8.0 10.0 6.0 13.0 14.0 6.0 13.0 12.0 13.0 11.0 12.0 18.0 GPA 1.0 1.6 1.2 2.1 2.6 1.8 2.6 2.0 3.2 2.6 3.0 3.6 Descriptive Statistics Mean GPA IQ study Std. Deviation N 2.2750 .79901 12 125.2500 9.22571 12 11.3333 3.44656 12 ANOVAb Model 1 Sum of Squares Regression Residual Total a. Predictors: (Constant), study, IQ b. Dependent Variable: GPA df Mean Square 6.389 2 3.194 .634 9 .070 7.023 11 F 45.353 Sig. .000a 2 Model Summary Model R Std. Error of the Square Estimate R Square .954a 1 Adjusted R .910 .890 .26539 a. Predictors: (Constant), study, IQ Correlations GPA Pearson Correlation Sig. (1-tailed) N GPA IQ study 1.000 .856 .829 IQ .856 1.000 .560 study .829 .560 1.000 . .000 .000 IQ .000 . .029 study .000 .029 . GPA 12 12 12 IQ 12 12 12 study 12 12 12 GPA Coefficientsa Standardized Unstandardized Coefficients Model 1 B (Constant) Std. Error -5.249 1.166 IQ .049 .010 study .118 .028 a. Dependent Variable: GPA Coefficients Beta t Sig. -4.501 .001 .570 4.717 .001 .509 4.209 .002 3 Coefficientsa Correlations Model 1 Zero-order Partial Part IQ .856 .844 .472 study .829 .814 .422 a. Dependent Variable: GPA (2) Write the regression equation below here. (1) What percent of the variance is unaccounted for by the above predictor variables? (2) From the above analysis, if we take the square root of the MS residual, what is that number called and what does it reflect? (2) Which predictor variable has the strongest relationship to Y and how do you know this (1) What percent of the total variability is uniquely accounted for by IQ (hint examine the part correlations) (1) What number is in the denominator of the t-test for testing the significance of the predictor study time? (2) With study time in the model, for each unit change in IQ how much of a change occurs in Y and in what direction. 4 (2) With IQ in the model, for each standard deviation change in Study time how much of a standard deviation change in Y occurs and in what direction. (1) What number is in the denominator of the t-test for testing the significance of the predictor IQ? 2. (10 Points) A statistics professor conducts a study to investigate the relationship between the performance of students on his exams and their anxiety. Ten students from his class are selected for the experiment. Just prior to taking the final exam, the 10 students are given an anxiety questionnaire. Here are final exam and anxiety scores for the students. Anxiety 28 41 35 39 31 42 50 46 45 37 Final Exam 82 58 63 89 92 64 55 70 51 72 X = 394 Y = 696 X2 = 15,946 XY = 26,819 Y2 = 50,248 a) Pearson r for these two variables is _________ b) Write the least squares regression equation using anxiety predicting the final exam. 5 c) If anxiety level was 20, what is the predicted final exam score. 97.303 d) Compute the Standard Error of estimate e) If we restricted the range on either Anxiety or final exam score, what is the most likely thing to happen assuming the relationship is linear. 3. (20 points) A large corporation is interested in predicting a measure of job satisfaction its employees. It has collected data on 15 employees who each supplied information on job satisfaction, level of responsibility, number of people supervised, rating of working environment and years of service. Satisfaction: Responsibility: No. supervised: Environment: Years of Service: 2 4 5 1 5 2 2 3 1 7 3 3 4 7 5 3 6 7 3 3 5 2 4 5 3 5 8 8 8 6 6 4 6 5 3 6 5 5 5 2 6 8 9 6 7 7 8 8 4 3 8 9 9 7 5 8 6 3 2 5 8 3 6 8 8 9 7 9 7 8 9 9 9 9 1 A simultaneous a multiple regression analysis was computed using years of service, environment, numb supervised and responsibility as predictors and satisfactory ratings as the dependent variable. Using the output below answer the questions for problem 4. Model Summary Model 1 R .697a R Square .486 Adjusted R Std. Error of the Square Estimate .281 a. Predictors: (Constant), yrsservice, numsuper, environment, Responsibility Coefficientsa 2.05723 6 Standardized Unstandardized Coefficients Model 1 B (Constant) Std. Error 1.669 2.032 .605 .428 -.334 environment yrsservice Responsibility numsuper Coefficients Beta t Sig. .822 .430 .624 1.414 .188 .537 -.311 -.622 .548 .486 .276 .514 1.758 .109 .070 .262 .063 .268 .794 a. Dependent Variable: satisfaction 1. With all four variables in the model what percent of the variance is accounted for? 2. With all other variables in the model, for each unit change in responsibility how much of a change occurs in Y and in what direction. 3. With all other variables in the model, for each standard deviation change in years of service how much of a standard deviation change in Y occurs and in what direction. 4. Which of the five predictor(s) accounts for a significant amount of the variance in Y? 5. Using the simultaneous multiple regression procedure, which of the five predictors accounts for the largest amount of the variance in Y and how do you know this? 6. What number from the output gives us the error in prediction (put an actual number in here) 7 7. Write the regression equation below here. 4. (6 points) What is collinearity and multicollinearity? Why is it a problem? Be specific and complete in your answer. 5. (8 points) describe what a partial and a part correlation is. Give an example of each and what they accomplish. 6. (5 points) What are the standardized regression coefficients and why do we need them? ____ a. b. c. d. 7. Satisfying the assumption of homoscedasticity allows you to _________. Interpret the standard error of estimate Calculate multiple R Calculate a standardized regression coefficient Decide who has been naughty or nice ____ 8. The farther the points on a scatter diagram fall from the regression line, the _________ between the scores. a. higher the correlation b. lower the correlation c. correlation doesn't change d. need more information ____ a. b. c. d. 9. The stronest degree of correlation shown below is _________. 0.75 -0.33 -0.87 0.15 8 ____ 10. If the correlation between two variables is 1.00 and the score of a given individual is 2.20 standard deviations above the mean on one of the variables, we would predict a score on the second variable of _________. a. 2.20 standard deviations below the mean b. 2.20 standard deviations above the mean c. more than 2.20 standard deviations above the mean