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Matakuliah
Tahun
: I0272 - STATISTIK PROBABILITAS
: 2009
KORELASI DAN REGRESI LINIER
Pertemuan 11
Materi
• Konsep dasar: korelasi dan regresi, data
berpasangan
• Model regresi linier (sederhana dan berganda)
• Estimasi parameter regresi linier sederhana
(Metode kuadrat terkecil)
Bina Nusantara University
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
Bina Nusantara University
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
Bina Nusantara University
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
Bina Nusantara University
6
The Least Squares Method
• Slope for the Estimated Regression Equation
 xi y i  (  xi  y i ) / n
b1 
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 = value of dependent variable for ith observation
i
_x = mean value for independent variable
y = mean value for dependent variable
n = total number of observations
Bina Nusantara University
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
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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
Bina Nusantara University
9
Contoh Soal: Reed Auto Sales
• Scatter Diagram
30
Cars Sold
25
20
y = 5x + 10
15
10
5
0
0
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1
2
TV Ads
3
4
10
The Coefficient of Determination
• Relationship Among SST, SSR, SSE
SST = SSR + SSE
2
2
^ )2
 ( y i  y )   ( y^i  y )   ( y i  y
i
• 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
Bina Nusantara University
11
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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12
The Correlation Coefficient
• Sample Correlation Coefficient
rxy  (sign of b1 ) Coefficien t of Determinat ion
rxy  (sign of b1 ) r 2
yˆ  b0  b1 x
where:
b1 = the slope of the estimated regression
equation
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13
Contoh Soal: Reed Auto Sales
• Sample Correlation Coefficient
rxy  (sign of b1 ) r
2
yˆ  10  5 x
rxy = + .8772
The sign of b1 in the equation
rxy = +.9366
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is “+”.
14