Matakuliah : L0104 / Statistika Psikologi
Tahun : 2008

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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• Model matematik
• Metode kuadrat terkecil
• Asumsi-asumsi model
• Pendugaan parameter regresi dan peramalan
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4

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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The Simple Linear Regression Model
• Simple Linear Regression Model y = β
0
+ β
1 x + ε
E( y ) = β
0
+ β
1 x
• Estimated Simple Linear Regression Equation y = b
0
+ b
1 x
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Least Squares Method
• Least Squares Criterion
 i
 y  i
)
2 where: yi = observed value of the dependent variable
^ for the i th observation yi = estimated value of the dependent variable for the i th observation
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The Least Squares Method
• Slope for the Estimated Regression Equation b
1

 x y
 x i
2
 ( 
  x x i i

2 y i
) /
) / n n
• y _ _
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_ where:
_ xi = value of independent variable for i th observation yi = value of dependent variable for i th 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
2
24
18
1
3
17
27
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Contoh Soal: Reed Auto Sales
• Slope for the Estimated Regression Equation b
1
= 220 - (10)(100)/5 = 5
24 - (10) 2 /5
• y -Intercept for the Estimated
Regression Equation b
0
= 20 - 5(2) = 10
• Estimated Regression Equation y = 10 + 5 x
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Contoh Soal: Reed Auto Sales
• Scatter Diagram
30
25
20
15
10
5
0
0 1
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2
TV Ads y = 5x + 10
3 4

The Coefficient of Determination
• Relationship Among SST, SSR, SSE
 (
SST = SSR + SSE y i
 y ) 2   ( y i
 y ) 2   ( y i
 y i
) 2
• Coefficient of Determination r 2 = 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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Contoh Soal: Reed Auto Sales
• Coefficient of Determination r 2 = SSR/SST = 100/114 = .8772
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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 r xy

(sign of b
1
) Coefficien t of Determinat ion r xy

(sign of b
1
) r
2 where: b 1 = the slope of the estimated regression y
 b
0
 b
1 x equation
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Contoh Soal: Reed Auto Sales
• Sample Correlation Coefficient r xy

(sign of b
1
) y
ˆ 
10

5 x r xy
= + .8772
The sign of b 1 in the equation is “+”.
r xy
= +.9366 r
2
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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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