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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
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