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

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

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

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

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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. : : ()      t n b sb bsbb tn 10-6 Hypothesis Tests about the Regression Relationship

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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 How Good is the Regression?

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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

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

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

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

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

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

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

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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 Use of the Regression Model for Prediction

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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]

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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]

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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

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

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

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 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 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