Simple Regression ©

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

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 (+)  ________________________   Kuat (-)Kuat (+)

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

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

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.

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..

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.

Linear Regression Model

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

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

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