ModelComparison_NormalCurve 13

# ModelComparison_NormalCurve 13 - Multiple Regression Review...

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Multiple Regression Review

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Correlations and Betas In multiple regression, a significant correlation does NOT mean the regression coefficient will be significant The correlation is between Y and X ONLY The coefficient is adjusted for the other X’s in the regression equation.
Correlations and Betas GPA and SAT r = .757, p = .015 GPA and Work r = -.861, p = .003 GPA and Study r = .896, p = .001 GPA and Health r = .671, p = .034 Coefficients a 2.560 .343 7.456 .005 .032 .046 .247 .689 .540 -.010 .005 -.525 -2.130 .123 .010 .015 .306 .627 .575 .002 .042 .014 .057 .958 (Constant) SAT Work Study Health Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients Sig. Dependent Variable: GPA a. GPA and SAT β = .247, p = .540 GPA and Work β = -.525, p = .123 GPA and Study β = .306, p = .575 GPA and Health β = .014, p = .958 From the Correlation Matrix From the Coefficient Table

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Coefficients as Weights Coefficients represent the “weight” each predictor brings to the prediction, controlling for the other predictors
Multiple Regression Equation: Standardized scores Coefficients a 2.560 .343 7.456 .005 .032 .046 .247 .689 .540 -.010 .005 -.525 -2.130 .123 .010 .015 .306 .627 .575 .002 .042 .014 .057 .958 (Constant) SAT Work Study Health Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: GPA a. Predicted Z Y = .247(SAT) + -.525(Work) + .306(Study) + .014(Health) Important! You can meaningfully compare the Beta’s ( β ’s) because they are standardized. Which beta has the most “weight”?

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Multiple Regression Equation: Unstandardized (raw) scores Coefficients a 2.560 .343 7.456 .005 .032 .046 .247 .689 .540 -.010 .005 -.525 -2.130 .123 .010 .015 .306 .627 .575 .002 .042 .014 .057 .958 (Constant) SAT Work Study Health Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: GPA a. Predicted Y = 2.560 + .032(SAT) + -.010(Work) + .010(Study) + .002(Health) Important! You can NOT meaningfully compare the B’s because they are NOT standardized. You can NOT determine which B has the most “weight”. Y-intercept
Multiple Regression Equation: p- values for coefficients Coefficients a 2.560 .343 7.456 .005 .032 .046 .247 .689 .540 -.010 .005 -.525 -2.130 .123 .010 .015 .306 .627 .575 .002 .042 .014 .057 .958 (Constant) SAT Work Study Health Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent Variable: GPA a. Important! You CAN meaningfully compare the p-values for the coefficients. Are any of the coefficients statistically significant? Do any of the variables add to the prediction ABOVE what the other variables add?

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Multiple Linear Regression Regression Coefficients and Coefficient of determination
Proportion of variance accounted for GPA SAT Study Habits The space in this circle represents variance of SAT’s. SAT’s vary across people. The space in this circle represents variance of GPA’s. GPA’s vary across people. Some of the variance in GPA’s can be accounted for by the variance in SAT’s. The space in this circle represents variance of Study Habits. Study Habits vary across people.

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## This note was uploaded on 05/26/2011 for the course PSCH 343 taught by Professor Victoriaharmon during the Spring '11 term at Ill. Chicago.

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ModelComparison_NormalCurve 13 - Multiple Regression Review...

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