Correlation & Regression

The Data SPSS-Data.htmhttp://core.ecu.edu/psyc/wuenschk/SPSS/ SPSS-Data.htm Corr_Regr –See Correlation and Regression Analysis: SPSSCorrelation and Regression Analysis: SPSS Master’s Thesis, Mike Sage, 2015 Cyberloafing = Age, Conscientiousness

Analyze, Correlate, Bivariate

Pearson Correlations CyberloafingAgeConscientiousness Cyberloafing Pearson Correlation ** ** Sig. (2-tailed) N51 Age Pearson Correlation-.462 ** Sig. (2-tailed) N51 Conscientiousness Pearson Correlation-.563 **.1431 Sig. (2-tailed) N51 **. Correlation is significant at the 0.01 level (2-tailed).

Spearman Correlations CyberloafingAgeConscientiousness Spearman's rho Cyberloafing Correlation Coefficient ** ** Sig. (2-tailed) N51 Age Correlation Coefficient ** Sig. (2-tailed) N51 Conscientiousness Correlation Coefficient ** Sig. (2-tailed) N51 **. Correlation is significant at the 0.01 level (2-tailed).

Analyze, Regression, Linear

Statistics

Plots

r =.1 is small,.3 medium,.5 large Model Summary b ModelRR Square Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), Conscientiousness b. Dependent Variable: Cyberloafing

Coefficients a ModelUnstandardized Coefficients Standardized Coefficients tSig. BStd. ErrorBeta 1 (Constant) Conscientiousness a. Dependent Variable: Cyberloafing Cyberloafing = (Conscientiousness) + error t Consc. = /7.288 = = 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

R2R2 Adding Age increased R 2 from.317 to.466. ModelRR Square Adjusted R Square a

ANOVA ANOVA a Model Sum of Squares df Mean Square FSig. 1 Regression b Residual Total

Coefficients ModelUnstandardized Coefficients BStd. Error 1 (Constant) Conscientiousness Age

Unstandardized Coefficients Cyberloaf = Consc -.28 Age When Consc and Age = 0, Cyber = 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. Z Cyber = 0 +  1 Consc +  2 Age

More Coefficients tSig.Correlations BetaZero-orderPartialPart Constant Conscie Age

Beta Weights Z Cyber = Consc -.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 = 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 = 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 R 2 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 R 2 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.

Coefficients a ModelCollinearity Statistics ToleranceVIF 1 Age Conscientiousness

Residuals Residuals Statistics a MinimumMaximumMean Std. Deviation N Predicted Value Residual Std. Predicted Value Std. Residual No standardized residuals beyond 3 SD.

Residuals Histogram

Residuals Plot

Put a CI on R 2 SPSS-Programs.htmhttp://core.ecu.edu/psyc/wuenschk/SPSS/ SPSS-Programs.htm CI-R2-SPSS.zip -- Construct Confidence Interval for R 2 from regression analysisCI-R2-SPSS.zip –Using SPSS to Obtain a Confidence Interval for R2 From Regression -- instructionsUsing SPSS to Obtain a Confidence Interval for R2 From Regression –NoncF.sav -- necessary data fileNoncF.sav –F2R2.sps -- see Smithson's WorkshopF2R2.spsSmithson's Workshop –NoncF3.sps -- syntax fileNoncF3.sps

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 Corr_Regr.sav 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