Analisis Varians Dwi Arah Pertemuan 22 Matakuliah: I0174 – Analisis Regresi Tahun: Ganjil 2007/2008.

Analisis Varians Dwi ArahPertemuan 22

Matakuliah : I0174 – Analisis RegresiTahun : Ganjil 2007/2008

Bina Nusantara

ELEMENTARY

Analisis Varians dwi arah tanpa interaksi Pendekatan regresi bagi bagi klasifikasi dua

arah

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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.) ^

^

^

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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

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(y - y) = (y - y) + (y - y)

(total deviation) = (explained deviation) + (unexplained deviation)

^ ^

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(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

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Definition

Coefficient of determination

the amount of the variation in y that is explained by the regression line

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Definition

r2 =explained variation

total variation

Coefficient of determinationThe amount of the variation in y that is explained by

the regression line

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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

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Prediction Intervals

DefinitionStandard error of estimate

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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

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Standard Error of Estimate

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Standard Error of Estimate

se = (y - y)2

n - 2

^

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Standard Error of Estimate

se = (y - y)2

n - 2

y2 - b0 y - b1 xyse = n - 2

or

Formula 9-6

^

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Prediction Interval for an Individual y

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y - E < y < y + E^ ^

Prediction Interval for an Individual y

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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

Bina Nusantara

y - E < y < y + E

n

where

n(x2) - (x)2

n(x0 - x)2

1 + +1

^

E = t2 se

^

x0 represents the given value of xt2 has n - 2 degrees of freedom

Prediction Interval for an Individual y