1. 1 Pertemuan 22 Regresi dan Korelasi Linier Sederhana-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1

2. 2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menyimpulkan hasil perhitungan model regresi linier sederhana dengan peramalan/pengambilan keputusan

3. 3 Outline Materi Uji Hipotesis tentang Hubungan Regresi Koefisien Determinasi Menggunakan Model Regresi untuk Peramalan

4. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-4 Example 10-1: = r SS XY SS X Y   51402852.4 40947557.8466855898 51402852.4 5232194329 9824 ()().. *Note: If  0, b 1 >0 Covariance and Correlation

5. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-5 H 0 :  = 0(No linear relationship) H 1 :  0(Some linear relationship) Test Statistic: Hypothesis Tests for the Correlation Coefficient

6. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-6 Y X Y X Y X Constant YUnsystematic VariationNonlinear Relationship A hypothesis test for the existence of a linear relationship between X and Y: H 0 H 1 Test statistic for the existence of a linear relationship between X and Y: (-) where is the least-squares estimate ofthe regression slope and() is the standard error of. When thenull hypothesis is true, the statistic has a distribution with- degrees offreedom. : : ()   1 0 1 0 2 1 1 111 2    t n b sb bsbb tn 10-6 Hypothesis Tests about the Regression Relationship

7. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-7 Hypothesis Tests for the Regression Slope

8. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-8 The coefficient of determination, r 2, is a descriptive measure of the strength of the regression relationship, a measure of how well the regression line fits the data.. { Y X { } Total Deviation Explained Deviation Unexplained Deviation Percentage of total variation explained by the regression. 10-7 How Good is the Regression?

9. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-9 Y X r 2 =0SSE SST Y X r 2 =0.90 SSESSE SST SSR Y X r 2 =0.50 SSE SST SSR The Coefficient of Determination

10. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-10 10-8 Analysis of Variance and an F Test of the Regression Model

11. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-11 Template (partial output) that displays Analysis of Variance and an F Test of the Regression Model

12. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-12 10-9 Residual Analysis and Checking for Model Inadequacies

13. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-13 Normal Probability Plot of the Residuals Flatter than Normal

14. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-14 Normal Probability Plot of the Residuals More Peaked than Normal

15. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-15 Normal Probability Plot of the Residuals More Positively Skewed than Normal More Positively Skewed than Normal

16. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-16 Normal Probability Plot of the Residuals More Negatively Skewed than Normal More Negatively Skewed than Normal

17. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-17 Point Prediction A single-valued estimate of Y for a given value of X obtained by inserting the value of X in the estimated regression equation. Prediction Interval For a value of Y given a value of X Variation in regression line estimate Variation of points around regression line For an average value of Y given a value of X Variation in regression line estimate Point Prediction A single-valued estimate of Y for a given value of X obtained by inserting the value of X in the estimated regression equation. Prediction Interval For a value of Y given a value of X Variation in regression line estimate Variation of points around regression line For an average value of Y given a value of X Variation in regression line estimate 10-10 Use of the Regression Model for Prediction

18. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-18 X Y X Y Regression line Upper limit on slope Lower limit on slope 1) Uncertainty about the slope of the regression line X Y X Y Regression line Upper limit on intercept Lower limit on intercept 2) Uncertainty about the intercept of the regression line Errors in Predicting E[Y|X]

19. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-19 X Y X Prediction Interval for E[Y|X] Y Regression line The prediction band for E[Y|X] is narrowest at the mean value of X. The prediction band widens as the distance from the mean of X increases. Predictions become very unreliable when we extrapolate beyond the range of the sample itself. The prediction band for E[Y|X] is narrowest at the mean value of X. The prediction band widens as the distance from the mean of X increases. Predictions become very unreliable when we extrapolate beyond the range of the sample itself. Prediction Interval for E[Y|X] Prediction band for E[Y|X]

20. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-20 Additional Error in Predicting Individual Value of Y 3) Variation around the regression line X Y Regression line X Y X Prediction Interval for E[Y|X] Y Regression line Prediction band for E[Y|X] Prediction band for Y

21. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-21 Prediction Interval for a Value of Y

22. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-22 Prediction Interval for the Average Value of Y

23. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-23 Template Output with Prediction Intervals

24. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 10-24 10-11 The Solver Method for Regression See the text for instructions. The solver macro available in EXCEL can also be used to conduct a simple linear regression. See the text for instructions.

25. 25 Penutup Regresi dan Korelasi linier Sederhana pada hakekatnya merupakan suatu pendekatan/model untuk mencari hubungan sebab akibat (secara linier) antara dua variabel, yaitu variabel bebas (variabel pengaruh) dan variabel tak bebas (variabel terpengaruh) yang selanjutnya dapat digunakan untuk peramalan atau prakiraan