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# Analisis Varians Dwi Arah Pertemuan 22

Analisis Varians Dwi Arah Pertemuan 22. Matakuliah : I0174 – Analisis Regresi Tahun : Ganjil 2007/2008. ELEMENTARY. Analisis Varians dwi arah tanpa interaksi Pendekatan regresi bagi bagi klasifikasi dua arah. Definitions. Total Deviation from the mean of the particular point ( x, y )

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## Analisis Varians Dwi Arah Pertemuan 22

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1. Analisis Varians Dwi ArahPertemuan 22 Matakuliah : I0174 – Analisis Regresi Tahun : Ganjil 2007/2008

2. ELEMENTARY • Analisis Varians dwi arah tanpa interaksi • Pendekatan regresi bagi bagi klasifikasi dua arah

3. 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.) ^ ^ ^

4. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Figure 9-9 Unexplained, Explained, and Total Deviation y (5, 19) • Unexplained deviation (y - y) Total deviation (y - y) (5, 13) ^ • Explained deviation (y - y) ^ • y = 9 (5, 9) ^ y = 3 + 2x x 0 1 2 3 4 5 6 7 8 9

5. (total deviation) = (explained deviation) + (unexplained deviation) ^ ^ (y - y) = (y - y) + (y - y)

6. (total deviation) = (explained deviation) + (unexplained deviation) ^ ^ (y - y) = (y - y) + (y - y) (total variation) = (explained variation) + (unexplained variation) ^ (y - y) 2 =  (y - y) 2 + (y - y) 2 ^ Formula 9-5

7. Definition Coefficient of determination the amount of the variation in y that is explained by the regression line

8. Definition Coefficient of determination The amount of the variation in y that is explained by the regression line explained variation r2 = total variation

9. Definition Coefficient of determination the amount of the variation in y that is explained by the regression line explained variation. r2 = total variation or simply square r (determined by Formula 9-1, section 9-2)

10. Prediction Intervals Definition Standard error of estimate

11. Prediction Intervals Definition Standard error of estimate 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 ^

12. Standard Error of Estimate

13. Standard Error of Estimate se = (y - y)2 ^ n- 2

14. Standard Error of Estimate se = (y - y)2 ^ n- 2 or y2 - b0  y - b1  xy se = n- 2 Formula 9-6

15. Prediction Interval for an Individual y

16. Prediction Interval for an Individual y y - E < y < y + E ^ ^

17. n(x2) - (x)2 Prediction Interval for an Individual y y - E < y < y + E ^ ^ where n(x0 - x)2 1 1 + + E = t2 se n

18. n(x2) - (x)2 Prediction Interval for an Individual y ^ ^ y - E < y < y + E where n(x0 - x)2 1 1 + + E = t2 se n x0 represents the given value of x t2 has n- 2 degrees of freedom

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