Quiz 8 Online Psych 541 Summer 2021 25 POINTS-due Monday 8/2 at 11:59 PM Key (25 points) This study looked at a number of factors that predicted the salary of faculty members at a university. The predictor variables are 1. Time in years since earning the Ph.D. 2. Number of Publications (NumofPub) 3. Number of times their articles are cited by others (numcit) 4. Gender The dependent variable is the current salary. A simultaneous multiple regression was run on the data and the output is listed below. Please use the data from the output to answer the questions below. Coefficientsa Model Unstandardized Coefficients Standardized Sig. Correlations Collinearity Statistics Coefficients B Std. Error Beta Zero-order Partia Part Tolerance VIE (Constant) 9587.350 2717.480 4.568 .000 TimesincePhD 857.006 287.946 .378 2.976 .004 608 367 .278 .541 1.848 NumofPubs 92.746 85.928 134 1.079 .285 506 .142 101 567 1.764 numcit 201.931 57.509 .357 3.511 .001 .550 .422 .328 .842 1.188 Gender -917.767 1859.936 - 047 -.493 624 -.201 ..065 - 046 950 1.053 a. Dependent Variable: salary ANOVAa Mode Sum of df Mean Square F Sig. Squares 2891959939.3 722989984.83 14.436 .000b Regression 32 2854659884.0 57 50081752.352 Residual 39 5746619823.3 6 Total 71 . Dependent Variable: salaryb. Predictors: (Constant), Gender, numcit, NumofPubs, TimesincePhD Model Summary Mode R R Square Adjusted R Std. Error of Square the Estimate .709a .503 .468 7076.84622 a. Predictors: (Constant), Gender, numcit, NumofPubs, TimesincePhD Correlation salary TimesincePhD NumofPubs numcit Gender salary 1.000 .608 506 .55 -.201 TimesincePhD 809' 1.000 .651 .373 -.210 Pearson Correlation NumofPubs .506 651 1.000 .333 .. 159 numcit .550 .373 .333 1.000 -. 149 Gender ..201 210 .. 159 .149 1.000 salary .000 000 .000 059 TimesincePhD .000 .000 .001 051 Sig. (1-tailed) NumofPubs .000 .000 .004 109 numcit .000 .001 .004 124 Gender .059 051 .109 124 salary 62 62 62 62 62 TimesincePhD 62 62 62 62 62 NumofPubs 62 62 62 62 N 62 numcit 62 62 62 32 62 Gender 62 62 62 62(4) Write the regression equation below here. 5. What percent of the variance (corrected for overination) is accounted for by all four predictor variables? (6) From the above analysis, if we take the square root of the MS residual, what is that number called and what does it reect? (7) Which predictor variable has the strongest relationship to salary and how do you know this (8) What percent of the total variability is uniquely accounted for by years since earning the Ph.D.? 9. What number is in the denominator of the ttest for testing the signicance of the predictor of gender? (10) With all other predictors in the model, for each unit change in Number of times their articles are cited by others (numcit) how much of a change occurs in salary and in what direction. 11. With all other predictors in the model, for each standard deviation change in Number of Publications (Numo'ub), how much of a standard deviation change in salary occurs and in what direction. 12. When testing the significance of the entire model, what number goes in the denominator of the F ratio? 13. Which of the predictor variables show the largest degree of correlation with each other? 14. (4 points) What is a regression coefficient and what does it tell you? What is a beta weight (standardized regression coefficient) and what does it tell you? What does a beta weight tell you that a regression coefficient does not? 15. Does the above analysis have any problems with multicollinearity? Cite 3 reasons to back up your claim