2. Regresi dan Korelasi Linear Pertemuan 19
Matakuliah : L0104 / Statistika Psikologi
Tahun : 2008
Regresi dan Korelasi Linear Pertemuan 19

3. Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
Mahasiswa akan dapat menganalisis dugaan parameter persamaan regresi, koefisien korelasi dan determinasi. 3
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4. Outline Materi Model matematik Metode kuadrat terkecil
Asumsi-asumsi model
Pendugaan parameter regresi dan peramalan 4
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5. 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
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6. The Simple Linear Regression Model
y = β0 + β1x + ε
Simple Linear Regression Equation
E(y) = β0 + β1x
Estimated Simple Linear Regression Equation
y = b0 + b1x ^ ^
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7. 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 ^
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8. 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 _ _ _ _
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9. 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
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10. Contoh Soal: Reed Auto Sales
Slope for the Estimated Regression Equation
b1 = (10)(100)/5 = 5
24 - (10)2/5
y-Intercept for the Estimated
Regression Equation
b0 = (2) = 10
Estimated Regression Equation
y = x ^
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11. Contoh Soal: Reed Auto Sales
Scatter Diagram
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12. 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 ^
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13. 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.
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14. The Correlation Coefficient
Sample Correlation Coefficient
where:
b1 = the slope of the estimated
regression
equation
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15. Contoh Soal: Reed Auto Sales
Sample Correlation Coefficient
The sign of b1 in the equation
is “+”.
rxy =
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16. Model Assumptions Assumptions About the Error Term ε
The error ε is a random variable with mean of zero.
The variance of ε , denoted by σ 2, is the same for all values of the independent variable.
The values of ε are independent.
The error ε is a normally distributed random variable.
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17. Selamat Belajar Semoga Sukses
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