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
Bina Nusantara University
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
Bina Nusantara University
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.
Bina Nusantara University
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
Bina Nusantara University
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
Bina Nusantara University
is “+”.
14