An Examination of Pearson Correlation Coefficients
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My dependent variable is engagement. And independent variables are amotivationintrinsic and extrinsic. There are a total of 242 observations for each variable in this data set. According to the table of descriptive analysis observe that the mean for engagement,intrinsic, extrinsic andamotivationis4.3233,4.839,5.5000 and1.6281 respectively. Themean for extrinsic is observed to be highest. The value of standard deviation for engagement,intrinsic, extrinsic andamotivationislow indicating that there mean is reliable.The assumption for multiple linear regression includes normality of residuals,homogeneityof error variance. Also, there should be no problem of multicolinearity in thedata. Multicolinearity occurs when the independent variables are strongly related to eachother. There should be no outlier in the data. Fox, J. (1997).Cook’s distance, D, is used to find outliers in a set of predictor variables. a Cook’s Dof more than 3 times the mean, μ, is a possible outlier. Here there are no outliers as value ofCooks’s D is less than 3 for all cases. Draper, N. R., & Smith, H. (2014).From the normal probability plot, Sshaped is formed indicating that assumption ofnormality of residuals is followed.From the column of variance inflation factor in the table of coefficient, I observe andthe value of variance inflation factor is less than 3 for all the three independent variables.This indicates that there is no problem of multicolinearity in data. The same is observedfrom the table of correlation, as there is no strong linear relationship observed between theindependent variables.Hence I can say that all the assumptions of multiple linear regressionis satisfied for this model. Seber, G. A., & Lee, A. J. (2012).
From the table of residual statistics observed at the mean of residual is zero and valueof standard deviation are 0.62.The scatter plot between standardized residuals andstandardized predicted value,I observed that all points are randomly distributed.Thisindicates that the variance is constant.This indicates that the assumption of homogeneityoferror variance is also followed.From the value of coefficient of determination, R^2 =0.721 I can say that, there is72.1% variation in engagement which is explained by all independent variables namelyamotivation, intrinsic and extrinsic. Regression equation is given by: engagement = 2.452+ .570* intrinsic .097* extrinsic .216* amotivation. Montgomery, D. C., Peck, E. A., &Vining, G. G. (2012).ReferencesBates, D. M., & Watts, D. G. (1988).Nonlinear regression analysis and its applications(Vol.2). New York: Wiley.Fox, J. (1997).Applied regression analysis, linear models, and related methods. SagePublications, Inc.Draper, N. R., & Smith, H. (2014).Applied regression analysis. John Wiley & Sons.Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012).Introduction to linear regressionanalysis(Vol. 821). John Wiley & Sons.Seber, G. A., & Lee, A. J. (2012).Linear regression analysis(Vol. 936). John Wiley & Sons.
AppendixDescriptiveStatisticsMeanStd.DeviationNengagement4.3233.90109242intrinsic4.83961.00242242extrinsic5.50001.13415242amotivation1.6281.82970242CorrelationsengagementintrinsicextrinsicamotivationPearson Correlationengagement1.000.685.034.412intrinsic.6851.000.136.337extrinsic.034.1361.000.012amotivation.412.337.0121.000Sig. (1tailed)engagement..000.301.000intrinsic.000..017.000extrinsic.301.017..429amotivation.000.000.429.Nengagement242242242242intrinsic242242242242extrinsic242242242242amotivation242242242242VariablesEntered/RemovedaModelVariablesEnteredVariablesRemovedMethod1amotivation, extrinsic, intrinsicb.Entera. Dependent Variable: engagementb. All requested variables entered.
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