Question:

(Examining the model summary table for Model 2 in the multiple regression output) did the addition of physical health score and psychological health score as predictors improve the fit of the model? (i.e., improve the amount of explained variability in happiness scores)? In your answer, report and interpret the R-square change for Model 2 and report the F change results.

Please see data attached below:

Multiple Regression Analysis Descriptive Statistics Overall Happiness Score (Sum of 4 Items) Overall Score on Self Esteem Scale (Sum of 10 Items) Physical Health (Health and Excercsie) Score (Sum of 6 items) Psychological Health Score (Sum of 7 items) Mean 19.00 29.69 21.38 27.13 Std . Deviation 4.956 5.220 6.810 4.542 90 90 90 90 Correlations Physical Overall Score Health Overall on Self- (Health and Psychological Happiness Esteem Scale Excercsie) Health Score Score (Sum (Sum of 10 Score (Sum (Sum of 7 of 4 Items) Items) of 6 items) items) Pearson Correlation Overall Happiness Score 1.000 585 .525 470 (Sum of 4 Items) Overall Score on Self- .585 1.000 .435 484 Esteem Scale (Sum of 10 Items) Physical Health (Health .525 .435 1.000 375 and Excercsie) Score (Sum of 6 items) Psychological Health 470 484 .375 1.000 Score (Sum of 7 items) Sig. (1-tailed) Overall Happiness Score .000 .000 000 (Sum of 4 Items) Overall Score on Self- 000 .000 000 Esteem Scale (Sum of 10 Items) Physical Health (Health 000 .000 000 and Excercsie) Score (Sum of 6 items) Psychological Health .000 000 000 Score (Sum of 7 items) N Overall Happiness Score 90 90 90 90 (Sum of 4 Items) Overall Score on Self- 90 90 90 90 Esteem Scale (Sum of 10 Items) Physical Health (Health 90 90 90 90 and Excercsie) Score (Sum of 6 items) Psychological Health 90 90 90 90 Score (Sum of 7 items)Variables Entered [Removedial Model 1 Variables Entered Overall Score on Self Esteem Scale (Sum (Bf 10 Items) Physical Heahh (Health and Excercsie) Score (Sum of 6 items), Psychological Health Score (Sum (Bf 7 items) Variables Re moved Method Enter Enter a. Dependent Variable: Overall Happiness Score (Sum of 4 Items) b. All requested variables entered. Model Summary Change Statistics Adjusted R Std. Error of R Square Model R R Square Square the Estimate Change F Change dfl df2 Sig. F Change 1 .5352' .342 .335 4.042 .342 45.786 1 88 .000 2 .675b .456 .437 3.718 .114 9.011 2 86 .000 a. Predictors: (Constant), Overall Score on SelfEsteem Scale (Sum of 10 Items) b. Predictors: (Constant), Overall Score on SelfEsteem Scale (Sum of 10 Items), Physical Health (Health and Excercsie) Score (Sum of 6 items), Psychological Health Score (Sum of 7 items) ANOVAa Sum of Model Squares df Mean Square F Sig. 1 Regression 748.121 1 748.121 45.786 .000b Residual 1437.879 88 16.340 Total 2186.000 89 2 Regression 997.245 3 332.415 24.048 .000c Residual 1188.755 86 13.823 Total 2186.000 89 a. Dependent Variable: Overall Happiness Score (Sum of 4 Items) b. Predictors: (Constant), Overall Score on SelfEsteem Scale (Sum of 10 Items) c. Predictors: (Constant), Overall Score on SelfEsteem Scale (Sum of 10 Items), Physical Health (Health and Excercsie) Score (Sum of 6 items), Psychological Health Score (Sum of 7 items) Coefficientsa Standardized Unstandardized Coefficients Coefficients Correlations Collinearity Statistics Model B Std. Error Beta t Sig. Zero-order Partial Part Tolerance VIF 1 (Constant) 2.511 2.474 1.015 313 Overall Score on Self- .555 082 .585 6.767 .000 585 .585 .585 1.000 1.000 Esteem Scale (Sum of 10 Items) 2 (Constant) -1.337 2.698 -.496 621 Overall Score on Self- .350 091 .369 3.855 .000 .585 .384 .307 .691 1.447 Esteem Scale (Sum of 10 Items) Physical Health (Health .216 066 297 3.293 .001 .525 .335 .262 776 1.289 and Excercsie) Score (Sum of 6 items) Psychological Health .196 .101 180 1.933 057 .470 .204 154 732 1.366 Score (Sum of 7 items) a. Dependent Variable: Overall Happiness Score (Sum of 4 Items) Excluded Variablesa Collinearity Statistics Partial Minimum Model Beta In Sig. Correlation Tolerance VIF Tolerance Physical Health (Health .334b 3.722 .000 371 811 1.233 811 and Excercsie) Score (Sum of 6 items) Psychological Health .244 2.540 .013 .263 .766 1.306 766 Score (Sum of 7 items a. Dependent Variable: Overall Happiness Score (Sum of 4 Items) b. Predictors in the Model: (Constant), Overall Score on Self-Esteem Scale (Sum of 10 Items)Excluded Variablesal Collinearity Statistics Partial Minimum Model Beta In t Sig. Correlation Tolerance VIF Tolerance 1 Physical Health (Health .334'3 3.722 .000 .371 .81 1 1.233 .81 1 and Excercsie) Score (Sum of 6 items) Psychological Health .244b 2.540 .013 .263 .766 1.306 .766 Score (Sum of 7 items) a. Dependent Variable: Overall Happiness Score (Sum of4 Items) b. Predictors in the Model: (Constant), Overall Score on SelfEsteem Scale (Sum of 10 Items) Collinearity Diagnosticsal Variance Proportions Physical Overall Score Health on Self (Health 510d Psychological Esteem Scale ExcerCSIe) Health Score Condition (Sum 0f 10 Score (Sum (Snm of 7 Model Dimension Eigenvalue Index (Constant) Items) Of 6 Items) ItEmS) 1 1 1.985 1.000 .01 .01 2 .015 11.525 .99 .99 2 1 3.916 1.000 .00 .00 .00 .00 2 .056 8.333 .05 .01 .93 .03 3 .015 16.281 .13 .97 .03 .28 4 .013 17.168 .82 .02 .03 .69 a. Dependent Variable: Overall Happiness Score (Sum of4 Items)