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

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

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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.) ^ ^ ^

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Bina Nusantara Total deviation ( y - y ) Unexplained deviation ( y - y ) Explained deviation ( y - y ) (5, 19) (5, 13) (5, 9) y = x ^ y = 9 ^ ^ y x Figure 9-9 Unexplained, Explained, and Total Deviation

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Bina Nusantara ( y - y ) = ( y - y ) + (y - y ) (total deviation) = (explained deviation) + (unexplained deviation) ^ ^

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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

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Bina Nusantara Definition Coefficient of determination the amount of the variation in y that is explained by the regression line

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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

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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

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Bina Nusantara Prediction Intervals Definition Standard error of estimate

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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

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Bina Nusantara Standard Error of Estimate

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

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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 ^

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Bina Nusantara Prediction Interval for an Individual y

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Bina Nusantara y - E < y < y + E ^ ^ Prediction Interval for an Individual y

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Bina Nusantara y - E < y < y + E n where n( x 2 ) - ( x) 2 n(x 0 - x) ^ E = t 2 s e ^ Prediction Interval for an Individual y

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Bina Nusantara y - E < y < y + E n where n( x 2 ) - ( x) 2 n(x 0 - x) ^ 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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