Matakuliah
Tahun
Versi
: I0134 – Metoda Statistika
: 2005
: Revisi
Pertemuan 21
Regresi dan Koefisien Korelasi
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat merumuskan
persamaan regresi dan koefisien korelasi.
2
Outline Materi
•
•
•
•
Persamaan regresi
Koefisien Korelasi
Uji t koefisien korelasi
Uji t koefisien korelasi
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
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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
_
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
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
9
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
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
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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
rxy  (sign of b1 ) Coefficien t of Determinat ion
rxy  (sign of b1 ) r 2
where:
b1 = the slope
yˆ  b0 ofb1 xthe estimated
regression
equation
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
is “+”.
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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