Quiz 8 Online Psych 541 Summer2021 25 POINTS-due Monday 8/2at 11:59 PM Key

(25points) 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.

Coefficients^a

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Correlations

Collinearity Statistics

B

Std. Error

Beta

Zero-order

Partial

Part

Tolerance

VIF

1

(Constant)

39587.350

2717.480

14.568

.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

ANOVA^a

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

2891959939.332

4

722989984.833

14.436

.000^b

Residual

2854659884.039

57

50081752.352

Total

5746619823.371

61

a. Dependent Variable: salary

b. Predictors: (Constant), Gender, numcit, NumofPubs, TimesincePhD

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.709^a

.503

.468

7076.84622

a. Predictors: (Constant), Gender, numcit, NumofPubs, TimesincePhD

Correlations

salary

TimesincePhD

NumofPubs

numcit

Gender

Pearson Correlation

salary

1.000

.608

.506

.550

-.201

TimesincePhD

.608

1.000

.651

.373

-.210

NumofPubs

.506

.651

1.000

.333

-.159

numcit

.550

.373

.333

1.000

-.149

Gender

-.201

-.210

-.159

-.149

1.000

Sig. (1-tailed)

salary

.

.000

.000

.000

.059

TimesincePhD

.000

.

.000

.001

.051

NumofPubs

.000

.000

.

.004

.109

numcit

.000

.001

.004

.

.124

Gender

.059

.051

.109

.124

.

N

salary

62

62

62

62

62

TimesincePhD

62

62

62

62

62

NumofPubs

62

62

62

62

62

numcit

62

62

62

62

62

Gender

62

62

62

62

62

(4) Write the regression equation below here.

5. What percent of the variance (corrected for overinflation) 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 reflect?

(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 t-test for testing the significance 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 (NumofPub),

how much of a standard deviation change in salary occurs and inwhat 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.