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

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

Bina Nusantara ELEMENTARY  Analisis Varians dwi arah tanpa interaksi  Pendekatan regresi bagi bagi klasifikasi dua arah

Bina Nusantara Definitions Total 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 Deviation the vertical distance y - y, which is the distance between the predicted y value and the horizontal line passing through the sample mean y Unexplained Deviation the 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 Total deviation ( y - y ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Unexplained deviation ( y - y ) Explained deviation ( y - y ) (5, 19) (5, 13) (5, 9) y = 3 + 2 x ^ y = 9 ^ ^ y x 0123456789 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 r 2 = explained variation total variation Coefficient of determination The amount of the variation in y that is explained by the regression line

Bina Nusantara Definition r 2 = explained variation. total variation or simply square r (determined by Formula 9-1, section 9-2) Coefficient of determination the amount of the variation in y that is explained by the regression line

Bina Nusantara Prediction Intervals Definition Standard 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 ^ Definition Standard error of estimate

Bina Nusantara Standard Error of Estimate

Bina Nusantara Standard Error of Estimate s e =  ( y - y ) 2 n - 2 ^

Bina Nusantara Standard Error of Estimate s e =  ( y - y ) 2 n - 2  y 2 - b 0  y - b 1  xy s e = 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(  x 2 ) - (  x) 2 n(x 0 - x) 2 1 + + 1 ^ E = t   2 s e ^ Prediction Interval for an Individual y

Bina Nusantara y - E < y < y + E n where n(  x 2 ) - (  x) 2 n(x 0 - x) 2 1 + + 1 ^ E = t   2 s e ^ x 0 represents the given value of x t   2 has n - 2 degrees of freedom Prediction Interval for an Individual y

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