Matakuliah
Tahun
: I0134 -Metode Statistika
: 2007
Korelasi dan Regresi Linear Sederhana
Pertemuan 25
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat menganalisis dugaan parameter
persamaan regresi, koefisien korelasi dan determinasi.
2
Outline Materi
•
•
•
•
Model matematik
Metode kuadrat terkecil
Asumsi-asumsi model
Pendugaan parameter regresi dan peramalan
3
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
4
The Simple Linear Regression Model
• Simple Linear Regression Model
y =  0 +  1x + 
• Simple Linear Regression Equation
E(y) = 0 + 1x
^
• Estimated Simple Linear Regression Equation
y = b0 + b1x
5
Least Squares Method
• Least Squares Criterion min  (y i  y i ) 2
where:
yi = observed value of the dependent variable
for the ith observation
yi = estimated value of the dependent variable
^ for the ith observation
6
The Least Squares Method
•
Slope for the Estimated Regression Equation
b1 
•
 xi y i  (  xi  y i ) / n
2
2
 xi  (  xi ) / n
y-Intercept for the Estimated Regression Equation
_
_
b0 = y - b1x
where:
xi = value of independent variable for ith observation
y_
i = value of dependent variable for ith observation
x = mean value for independent variable
_
y = mean value for dependent variable
n = total number of observations
7
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
1
3
2
1
3
Number of Cars Sold
14
24
18
17
27
8
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
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Contoh Soal: Reed Auto Sales
• Scatter Diagram
30
Cars Sold
25
20
y = 5x + 10
15
10
5
0
0
1
2
TV Ads
3
4
10
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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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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The Correlation Coefficient
• Sample Correlation Coefficient
where:
b1 = the slope of the estimated regression
equation yˆ  b0  b1 x
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Contoh Soal: Reed Auto Sales
• Sample Correlation Coefficient
yˆ  10  5 x
2
r

(sign
of
b
)
r
The sign of b1 in the equation xy
is “+”.
1
rxy = + .8772
rxy = +.9366
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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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• Selamat Belajar Semoga Sukses.
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