Simple Regression ©. Null Hypothesis The analysis of business and economic processes makes extensive use of relationships between variables.

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1 Simple Regression ©

2 Null Hypothesis The analysis of business and economic processes makes extensive use of relationships between variables.

3 Analisis Regresi adalah studi ketergantungan dari satu variabel dependent pada satu atau lebih variabel independent untukmemperkirakan/ meramalkan nilai rata-rata Y jika nilai X diketahui. Regresi dan Korelasi Regresi bukan hubungan (korelasi) sebab akibat dan bukan exact relationship. Analisis Korelasi ( r ) bertujuan untuk mengukur kuat lemahnya hubungan linier antara dua variabel. -1 ≤ r ≤ +1 Lemah (-)Lemah (+) ------------  ------------ ________________________ - 1 0 + 1  --------------------------  Kuat (-)Kuat (+)

4 Correlation Analysis correlation coefficient The correlation coefficient is a quantitative measure of the strength of the linear relationship between two variables.

5 Linear Regression Model LINEAR REGRESSION POPULATION EQUATION MODEL Where  0 and  1 are the population model coefficients and  is a random error term.

6 Linear Regression Outcomes Linear regression provides two important results: 1.Predicted values of the dependent or endogenous variable as a function of an independent or exogenous variable. 2.Estimated marginal change in the endogenous variable that results from a one unit change in the independent or exogenous variable.

7 Least Squares Procedure The Least-squares procedure obtains estimates of the linear equation coefficients b 0 and b 1, in the model by minimizing the sum of the squared residuals e i This results in a procedure stated as Choose b 0 and b 1 so that the quantity is minimized. We use differential calculus to obtain the coefficient estimators that minimize SSE..

8 Least-Squares Derived Coefficient Estimators The slope coefficient estimator is And the constant or intercept indicator is We also note that the regression line always goes through the mean X, Y.

9 Linear Regression Model

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11 Excel Output for Retail Sales Model The regression equation is Y Retail Sales = 1922 + 0.382 X Income SSRSSESSTMSR MSE b0b0 b1b1 s b1 t b1 sese

12 Uji Hipotesa digunakan untuk menguji statement tertentu tentang populasi Langkah-langkah dalam uji t : i.Memformulasikan H o dan H a H o : b i = 0 H a : b i ≠ 0 ii.Menghitung distribusi probabilitas : t hitung = b i S b i iii.Memilih level of significant α  1%; 5%; 10%  t tabel t α/2, n-k iv.Keputusan : Terima H o : ii < iii Tolak H o : ii > iii

13 Langkah-langkah dalam uji F : i.Memformulasikan H o dan H a H o : b 1 =b 2 =b 3 =….b k = 0 H a : setidaknya salah satu b i ≠ 0 ii.Menghitung distribusi probabilitas : F hitung = RSS/(k-1) ESS/(n-k) iii.Memilih level of significant α  1%;5%;10%  F tabel F tabel  F k-1;n-k iv.Keputusan : Terima H o : ii < iii Tolak H o : ii > iii