Bina Nusantara
ELEMENTARY
Analisis Varians dwi arah tanpa interaksi Pendekatan regresi bagi bagi klasifikasi dua
arah
Bina Nusantara
DefinitionsTotal Deviation from the mean of the particular point (x, y)
the vertical distance y - y, which is the distance between the point (x, y) and the horizontal line passing through the sample mean y
Explained Deviationthe vertical distance y - y, which is the distance between the predicted y value and the horizontal line passing through the sample mean y
Unexplained Deviationthe vertical distance y - y, which is the vertical distance between the point (x, y) and the regression line. (The distance y - y is also called a residual, as defined in Section 9-3.) ^
^
^
Bina Nusantara
Totaldeviation
(y - y)
01
23
456789
10
1112
131415
161718
1920
•
•
•
Unexplaineddeviation
(y - y)
Explaineddeviation
(y - y)
(5, 19)
(5, 13)
(5, 9)
y = 3 + 2x^
y = 9
^
^
y
x0 1 2 3 4 5 6 7 8 9
Figure 9-9 Unexplained, Explained, and Total Deviation
Bina Nusantara
(y - y) = (y - y) + (y - y)
(total deviation) = (explained deviation) + (unexplained deviation)
^ ^
Bina Nusantara
(y - y) = (y - y) + (y - y)
(total deviation) = (explained deviation) + (unexplained deviation)
(total variation) = (explained variation) + (unexplained variation)
(y - y) 2
= (y - y) 2
+ (y - y) 2^ ^
^ ^
Formula 9-5
Bina Nusantara
Definition
Coefficient of determination
the amount of the variation in y that is explained by the regression line
Bina Nusantara
Definition
r2 =explained variation
total variation
Coefficient of determinationThe amount of the variation in y that is explained by
the regression line
Bina Nusantara
Definition
r2 =explained variation.
total variation
or
simply square r(determined by Formula 9-1, section 9-2)
Coefficient of determinationthe amount of the variation in y that is explained by
the regression line
Bina Nusantara
a measure of the differences (or distances) between the observed sample y values and
the predicted values y that are obtained using the regression equation
Prediction Intervals
^
DefinitionStandard error of estimate
Bina Nusantara
Standard Error of Estimate
se = (y - y)2
n - 2
y2 - b0 y - b1 xyse = n - 2
or
Formula 9-6
^
Bina Nusantara
y - E < y < y + E
n
where
n(x2) - (x)2
n(x0 - x)2
1 + +1
^
E = t2 se
^
Prediction Interval for an Individual y
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