Correlation & Regression

The Data

• http://core.ecu.edu/psyc/wuenschk/SPSS/SPSS-Data.htm

• Corr_Regr– See Correlation and Regression Analysis:

SPSS

• Master’s Thesis, Mike Sage, 2015• Cyberloafing = Age, Conscientiousness

Analyze, Correlate, Bivariate

Pearson Correlations

  Cyberloafing Age Conscientiousness

Cyberloafing

Pearson Correlation 1 -.462** -.563**

Sig. (2-tailed)   .001 .000

N 51 51 51

Age

Pearson Correlation -.462** 1 .143

Sig. (2-tailed) .001   .317

N 51 51 51

Conscientiousness

Pearson Correlation -.563** .143 1

Sig. (2-tailed) .000 .317  

N 51 51 51

**. Correlation is significant at the 0.01 level (2-tailed).

Spearman Correlations

  Cyberloafing Age Conscientiousness

Spearman's rho

Cyberloafing

Correlation Coefficient 1.000 -.431** -.551**

Sig. (2-tailed) . .002 .000

N 51 51 51

Age

Correlation Coefficient -.431** 1.000 .110

Sig. (2-tailed) .002 . .442

N 51 51 51

Conscientiousness

Correlation Coefficient -.551** .110 1.000

Sig. (2-tailed) .000 .442 .

N 51 51 51

**. Correlation is significant at the 0.01 level (2-tailed).

Analyze, Regression, Linear

Statistics

Plots

563.317.2 rr

r = .1 is small, .3 medium, .5 large

Model Summaryb

Model R R Square Adjusted R Square

Std. Error of the Estimate

1 .563a .317 .303 7.677a. Predictors: (Constant), Conscientiousness

b. Dependent Variable: Cyberloafing

Coefficientsa

Model Unstandardized Coefficients

Standardized Coefficients

t Sig.

 

B Std. Error Beta  

1(Constant) 57.039 7.288   7.826 .000  

Conscientiousness -.864 .181 -.563 -4.768 .000  a. Dependent Variable: Cyberloafing

Cyberloafing = 57.039 - .864(Conscientiousness) + error

tConsc. = 57.039/7.288 = 7.826 = SQRT(22.736) = SQRT(F)

Residuals Histogram

Graphs, Scatter, Simple, Define

Chart Editor, Elements, Fit Line at Total, Method = Linear, Close

Construct a Confidence Interval for

the calculator at Vassar

Trivariate Analysis

Statistics

Plots

R2

• Adding Age increased R2 from .317 to .466.

Model R R Square Adjusted R Square

1 .682a .466 .443

ANOVA

ANOVAa

Model Sum of Squares

df Mean Square

F Sig.

1

Regression 1968.029 2 984.015 20.906 .000b

Residual 2259.304 48 47.069    

Total 4227.333 50      

Coefficients

Model Unstandardized Coefficients

B Std. Error

1

(Constant) 64.066 6.792

Conscientiousness -.779 .164

Age -.276 .075

Unstandardized Coefficients

• Cyberloaf = 64.07 -.78 Consc - .28 Age• When Consc and Age = 0, Cyber = 64.07• Holding Age constant, each one point

increase in Consc produces a .78 point decrease in Cyberloafing.

• Holding Consc constant, each one point increase in Age produces a .28 point decrease in Cyberloafing.

How Large are these Effects?

• Is a .78 drop in Cyberloafing a big drop or a small drop?

• When the units of measurement are arbitrary and not very familiar to others, best to standardize the coefficients to mean 0, standard deviation 1.

• ZCyber = 0 + 1Consc + 2Age

More Coefficients

    t Sig. Correlations

  Beta Zero-order Partial Part

Constant  9.433 .000

     

Conscie-.507 -4.759 .000 -.563 -.566 -.502

Age-.389 -3.653 .001 -.462 -.466 -.386

Beta Weights

• ZCyber = 0 -.51Consc - .39Age

• Holding Age constant, each one SD increase in Conscientiousness produces a .51 SD decrease in Cyberloafing

• Holding Conscientiousness constant, each one SD increase in Age produces a .39 SD decrease in Cyberloafing.

Semi-Partial Correlations

• The correlation between all of Cyberloafing and that part of Conscientiousness that is not related to Age = -.50.

• The correlation all of Cyberloafing and that part of Age that is not related to Conscientiousness = -.39.

Partial Correlations

• The correlation between that part of Cyberloafing that is not related to Age and that part of Conscientiousness that is not related to Age = -.57.

• The correlation between that part of Cyberloafing that is not related to Conscientiousness and that part of Age that is not related to Conscientiousness= -.47.

Multicollinearity

• The R2 between any one predictor and the remaining predictors is very high.

• Makes the solution unstable.• Were you to repeatedly get samples from

the same population, the regression coefficients would vary greatly among samples

Collinearity Diagnostics

• Tolerance, which is simply 1 minus the R2

between one predictor and the remaining predictors. Low (.1) is troublesome.

• VIF, the Variance Inflation Factor, is the reciprocal of tolerance. High (10) is troublesome.

Coefficientsa

Model Collinearity Statistics

Tolerance VIF

1

Age .980 1.021

Conscientiousness .980 1.021

ResidualsResiduals Statisticsa

  Minimum Maximum Mean Std. Deviation

N

Predicted Value 10.22 35.41 22.67 6.274 51

Residual -17.344 15.153 .000 6.722 51

Std. Predicted Value -1.983 2.032 .000 1.000 51

Std. Residual -2.528 2.209 .000 .980 51

No standardized residuals beyond 3 SD.

Residuals Histogram

Residuals Plot

Put a CI on R2

• http://core.ecu.edu/psyc/wuenschk/SPSS/SPSS-Programs.htm

• CI-R2-SPSS.zip -- Construct Confidence Interval for R2 from regression analysis– Using SPSS to Obtain a Confidence Interval f

or R2 From Regression -- instructions

– NoncF.sav -- necessary data file– F2R2.sps -- see Smithson's Workshop– NoncF3.sps -- syntax file

Open NoncF.sav

• Enter the observed value of F and degrees of freedom.

Open and Run the Syntax

Look Back at .sav File

Why You Need Inspect Scatterplots

• Data are at http://core.ecu.edu/psyc/wuenschk/SPSS/Corr_Regr.sav

• Four sets of bivariate data.• Bring into SPSS and Split File by “set.”

Predict Y from X in Four Different Data Sets