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

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

Prediction Intervals

DefinitionStandard error of estimate

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

Bina Nusantara

Standard Error of Estimate

se = (y - y)2

n - 2

^

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

Prediction Interval for an Individual y

Bina Nusantara

y - E < y < y + E^ ^

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

^

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