The total sum of squares, i.e. the

The total sum of squares, i.e. the left-hand side of Eq. (5.12.1), is clearly fixed once
the experimental yi values have been determined. A line fitting these experimental
points closely will be obtained when the variation due to regression (the first term on
the right-hand side of Eq. (5.12.1) is as large as possible. The variation about regression
(also called the residual SS as each component of the right-hand term in the
equation is a single residual) should be as small as possible. The method is quite general
and can be applied to straight line regression problems as well as to curvilinear
regression. Table 5.1 (see p. 133) shows the Excel® output for a linear plot used to compare
two analytical methods, including an ANOVA table set out in the usual way. The
total number of degrees of freedom (19 in that example) is, as usual, one less than the
number of measurements (20), as the y-residuals always add up to zero. For a straight
line graph we have to determine only one coefficient (b) for a term that also contains x,
so the number of degrees of freedom due to regression is 1. Thus there are (n 2)18
degrees of freedom for the residual variation. The mean square (MS) values are determined
as in previous ANOVA examples, and the F-test is applied to the two mean
squares as usual. The F-value obtained is very large, as there is an obvious relationship
between x and y, so the regression MS is much larger than the residual MS.

The total sum of squares, i.e. the left-hand side of Eq. (5.12.1), is clearly fixed once
the experimental yi values have been determined. A line fitting these experimental
points closely will be obtained when the variation due to regression (the first term on
the right-hand side of Eq. (5.12.1) is as large as possible. The variation about regression
(also called the residual SS as each component of the right-hand term in the
equation is a single residual) should be as small as possible. The method is quite general
and can be applied to straight line regression problems as well as to curvilinear
regression. Table 5.1 (see p. 133) shows the Excel® output for a linear plot used to compare
two analytical methods, including an ANOVA table set out in the usual way. The
total number of degrees of freedom (19 in that example) is, as usual, one less than the
number of measurements (20), as the y-residuals always add up to zero. For a straight
line graph we have to determine only one coefficient (b) for a term that also contains x,
so the number of degrees of freedom due to regression is 1. Thus there are (n  2)18
degrees of freedom for the residual variation. The mean square (MS) values are determined
as in previous ANOVA examples, and the F-test is applied to the two mean
squares as usual. The F-value obtained is very large, as there is an obvious relationship
between x and y, so the regression MS is much larger than the residual MS.

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The total sum of squares, i.e. the left-hand side of Eq. (5.12.1), is clearly fixed oncethe experimental yi values have been determined. A line fitting these experimentalpoints closely will be obtained when the variation due to regression (the first term onthe right-hand side of Eq. (5.12.1) is as large as possible. The variation about regression(also called the residual SS as each component of the right-hand term in theequation is a single residual) should be as small as possible. The method is quite generaland can be applied to straight line regression problems as well as to curvilinearregression. Table 5.1 (see p. 133) shows the Excel® output for a linear plot used to comparetwo analytical methods, including an ANOVA table set out in the usual way. Thetotal number of degrees of freedom (19 in that example) is, as usual, one less than thenumber of measurements (20), as the y-residuals always add up to zero. For a straightline graph we have to determine only one coefficient (b) for a term that also contains x,so the number of degrees of freedom due to regression is 1. Thus there are (n 2)18degrees of freedom for the residual variation. The mean square (MS) values are determinedas in previous ANOVA examples, and the F-test is applied to the two meansquares as usual. The F-value obtained is very large, as there is an obvious relationshipbetween x and y, so the regression MS is much larger than the residual MS.

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Total jumlah kuadrat, yaitu sisi kiri persamaan. (5.12.1), jelas sekali tetap
nilai yi eksperimental telah ditentukan. Sebuah garis pas ini eksperimental
poin erat akan diperoleh ketika variasi karena regresi (istilah pertama di
sisi kanan persamaan. (5.12.1) adalah sebesar mungkin. Variasi tentang regresi
(juga disebut SS sisa karena setiap komponen dari jangka kanan di
persamaan merupakan sisa tunggal) harus sekecil mungkin. Metode ini cukup umum
dan dapat diterapkan untuk masalah regresi garis lurus serta lengkung
regresi. Tabel 5.1 (lihat hal . 133) menunjukkan output Excel untuk plot linear digunakan untuk membandingkan
dua metode analisis, termasuk meja ANOVA ditetapkan dengan cara yang biasa. The
Jumlah derajat kebebasan (19 dalam contoh itu) adalah, seperti biasa, satu kurang dari
jumlah pengukuran (20), sebagai y-residual selalu menambahkan hingga nol. Untuk lurus
grafik garis kita harus menentukan satu koefisien (b) untuk jangka waktu yang juga berisi x,
sehingga jumlah derajat kebebasan karena regresi adalah 1. Jadi ada (n 2?)? 18
derajat kebebasan untuk variasi residual. Mean square (MS) nilai-nilai yang ditentukan
seperti dalam contoh ANOVA sebelumnya, dan F-test diterapkan untuk dua rata-rata
kotak seperti biasa. F-nilai yang diperoleh sangat besar, karena ada hubungan yang jelas
antara x dan y, sehingga regresi MS jauh lebih besar daripada MS sisa.

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