Uji Kelinearan dan Keberartian Regresi Pertemuan 02

1. Uji Kelinearan dan Keberartian RegresiPertemuan 02 Matakuliah : I0174 – Analisis Regresi Tahun : Ganjil 2007/2008

2. Uji Kelinieran dan Keberartian Regresi • Anova pada regresi Sederhana • Selang Kepercayaan Parameter Regresi • Uji Independen Antar Peubah

3. Measures of Variation: The Sum of Squares SST =SSR + SSE Total Sample Variability Unexplained Variability = Explained Variability +

4. Measures of Variation: The Sum of Squares (continued) • SST = Total Sum of Squares • Measures the variation of the Yi values around their mean, • SSR = Regression Sum of Squares • Explained variation attributable to the relationship between X and Y • SSE = Error Sum of Squares • Variation attributable to factors other than the relationship between X and Y

5. Measures of Variation: The Sum of Squares (continued) Y  SSE =(Yi-Yi )2 _  SST =(Yi-Y)2 _  SSR = (Yi -Y)2 _ Y X Xi

6. Venn Diagrams and Explanatory Power of Regression Variations in Sales explained by the error term or unexplained by Sizes Variations in store Sizes not used in explaining variation in Sales Sales Variations in Sales explained by Sizes or variations in Sizes used in explaining variation in Sales Sizes

7. The ANOVA Table in Excel

8. Measures of VariationThe Sum of Squares: Example Excel Output for Produce Stores Degrees of freedom SST Regression (explained) df SSE Error (residual) df SSR Total df

9. The Coefficient of Determination • Measures the proportion of variation in Y that is explained by the independent variable X in the regression model

10. Venn Diagrams and Explanatory Power of Regression Sales Sizes

11. Coefficients of Determination (r 2) and Correlation (r) r2 = 1, Y r = +1 Y r2 = 1, r = -1 ^ Y = b + b X i 0 1 i ^ Y = b + b X i 0 1 i X X r2 = 0, r = 0 r2 = .81, r = +0.9 Y Y ^ ^ Y = b + b X Y = b + b X i 0 1 i i 0 1 i X X

12. Standard Error of Estimate • Measures the standard deviation (variation) of the Y values around the regression equation

13. Measures of Variation: Produce Store Example Excel Output for Produce Stores n Syx r2 = .94 94% of the variation in annual sales can be explained by the variability in the size of the store as measured by square footage.

14. Linear Regression Assumptions • Normality • Y values are normally distributed for each X • Probability distribution of error is normal • Homoscedasticity (Constant Variance) • Independence of Errors

15. Consequences of Violationof the Assumptions • Violation of the Assumptions • Non-normality (errornot normally distributed) • Heteroscedasticity (variance not constant) • Usually happens in cross-sectional data • Autocorrelation (errors are not independent) • Usually happens in time-series data • Consequences of Any Violation of the Assumptions • Predictions and estimations obtained from the sample regression line will not be accurate • Hypothesis testing results will not be reliable • It is Important to Verify the Assumptions

16. Variation of Errors Aroundthe Regression Line f(e) • Y values are normally distributed around the regression line. • For each X value, the “spread” or variance around the regression line is the same. Y X2 X1 X Sample Regression Line

17. Residual Analysis • Purposes • Examine linearity • Evaluate violations of assumptions • Graphical Analysis of Residuals • Plot residuals vs. X and time