Korelasi dan Regresi Linear Sederhana Pertemuan 25 Matakuliah : I0134 -Metode Statistika Tahun : 2007 Korelasi dan Regresi Linear Sederhana Pertemuan 25

Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menganalisis dugaan parameter persamaan regresi, koefisien korelasi dan determinasi.

Outline Materi Model matematik Metode kuadrat terkecil Asumsi-asumsi model Pendugaan parameter regresi dan peramalan

Simple Linear Regression Simple Linear Regression Model Least Squares Method Coefficient of Determination Model Assumptions Testing for Significance Using the Estimated Regression Equation for Estimation and Prediction Computer Solution Residual Analysis: Validating Model Assumptions Residual Analysis: Outliers and Influential Observations

The Simple Linear Regression Model y = 0 + 1x +  Simple Linear Regression Equation E(y) = 0 + 1x Estimated Simple Linear Regression Equation y = b0 + b1x ^

Least Squares Method Least Squares Criterion where: yi = observed value of the dependent variable for the ith observation yi = estimated value of the dependent variable ^

The Least Squares Method Slope for the Estimated Regression Equation y-Intercept for the Estimated Regression Equation b0 = y - b1x where: xi = value of independent variable for ith observation yi = value of dependent variable for ith observation x = mean value for independent variable y = mean value for dependent variable n = total number of observations _ _ _ _

Contoh Soal: Reed Auto Sales Simple Linear Regression Reed Auto periodically has a special week-long sale. As part of the advertising campaign Reed runs one or more television commercials during the weekend preceding the sale. Data from a sample of 5 previous sales are shown below. Number of TV Ads Number of Cars Sold 1 14 3 24 2 18 1 17 3 27

Contoh Soal: Reed Auto Sales Slope for the Estimated Regression Equation b1 = 220 - (10)(100)/5 = 5 24 - (10)2/5 y-Intercept for the Estimated Regression Equation b0 = 20 - 5(2) = 10 Estimated Regression Equation y = 10 + 5x ^

Contoh Soal: Reed Auto Sales Scatter Diagram

The Coefficient of Determination Relationship Among SST, SSR, SSE SST = SSR + SSE Coefficient of Determination r2 = SSR/SST where: SST = total sum of squares SSR = sum of squares due to regression SSE = sum of squares due to error ^

Contoh Soal: Reed Auto Sales Coefficient of Determination r2 = SSR/SST = 100/114 = .8772 The regression relationship is very strong since 88% of the variation in number of cars sold can be explained by the linear relationship between the number of TV ads and the number of cars sold.

The Correlation Coefficient Sample Correlation Coefficient where: b1 = the slope of the estimated regression equation

Contoh Soal: Reed Auto Sales Sample Correlation Coefficient The sign of b1 in the equation is “+”. rxy = +.9366

Model Assumptions Assumptions About the Error Term  The error  is a random variable with mean of zero. The variance of  , denoted by  2, is the same for all values of the independent variable. The values of  are independent. The error  is a normally distributed random variable.

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