Dependent VS independent variable

Transkripsi

1 Kuswanto-2012

2 !" #!! $!! %! & '%

3 Dependent VS independent variable Indep. Var. (X) Dep. Var (Y) Regression Equation Fertilizer doses Yield y = b0 + b1x Evaporation Rain fall y = b0+b1x+b2x 2 Sum of Leave pod yield Etc

4 Regression vs Correlation The relationship between correlation and regression analysis is intertwined (saling terkait). Strictly speaking regression analysis is done where one variable is dependent on the other variable. In cases where both variables are independent (leave number, plant height, example), correlation analysis is appropriate.

5 Bentuk umum persamaan regresi In general, the equation for a straight line is : Y = b0 + b1x + e where b0 = intercept (set X = 0) (some books written a) b1 = slope of line Or amount of change in Y with each unit change in X, Also called regression coefficient Y b1 bo Y = b0 + b1x 0 X

6 yield fertilizer!

7 yield fertilizer The distance from each point to the regression line is known as the residual.

8 yield fertilizer Since some of these deviations are positive and some negative, we use the sum of their squares (just like with SD and variance). Known as least squares method.

9 Best-fit Line Aim of linear regression is to fit a straight line, = b0 + b1x, to data that gives best prediction of y for any value of x This will be the line that minimises distance between data and fitted line, i.e. = b0 + b1x the residuals intercept slope =, predicted value = y i, true value = residual error

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11 Menghitung Koefisien Regresi b1 The regression coefficient (slope) is calculated by xy b1 = x 2 Where xy = (x i x)(y i y) = XY {(X)(Y)}/n And x 2 = (x i x) 2 = X 2 (X) 2 /n So, b1 = XY {(X)(Y)}/n X 2 (X) 2 /n So for each data point (x, y) multiply the deviation of x from the mean x by the deviation of y from the mean y.

12 Menghitung intersep (bo) It can also be shown that the point (X mean, Y mean) always lies on the best fit line. Y = b0 + b1x Substituting, we get Y = b0 + b1x Therefore, to calculate intercept, a rearrange: bo= Y b1x Now, we have formulas to calculate b0 and b1

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14 Perhatikan gugusan data pada diagram pencar ini Y X Dari gambar tersebut sebenarnya X tidak mempengaruhi Y, karena garis yang paling tepat Untuk menggambarkan adalah garis lurus, karena kemungkinan nilai b1=0 What is the chance of selecting at random a set of points where the slope (b1) does not = 0

15 Uji nyata regresi Untuk menguji bentuk hubungan yang digambarkan oleh persamaan regresi ANOVA testing may be done. Anova untuk menguji taraf nyata regresi So Ho: b1 = 0 (that X does not affect Y) HA: b1 0 (that X does affect Y) Y F = KT Regresi KT galat X

16 b1x i y i BENTUK ANOVA REGRESI y i 2 Dimana, JK total = y 2 i = (Yi Y) 2 = Y 2 (Y) 2 /n Dimana, JK regresi = b1xy = b1(xi X)(Yi Y) = b1{xy (X)(Y)/n} And the rest of the variation is the residuals (source = residual) JK sisa = JK total JK Regresi

17 Koefisien Determinasi R 2 = JKregresi JK Total! " # $ % &!

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19 Cara mencari persamaan regresi ) * XY {(X)(Y)}/n b1 = X 2 (X) 2 /n! " # $ "# %& ' ( & ++, - % ' (-,-

20 Cara perhitungan No Age (X) Weight (Y) XY X 2 Y Sum Mean Buat tabel untuk menghitung jumlah tiap-tiap komponen. Kemudian isilah tabel tersebut. Hitung perkalian X dengan Y

21 Cara perhitungan No Age (X) Weight (Y) XY X 2 Y Sum Mean Hitung kuadrat dari X

22 Cara perhitungan No Age (X) Weight (Y) XY X 2 Y Sum Mean Hitunglah kuadrat dari Y

23 Cara perhitungan No Age (X) Weight (Y) XY X 2 Y Sum Mean Hitunglah jumlah masing-masing komponen

24 Cara perhitungan No Age (X) Weight (Y) XY X 2 Y Sum Mean Hitung nilai rata-rata X dan Y untuk menghitung intersep

25 Tabel lengkap, kemudian masukkan ke rumus. No Age (X) Weight (Y) XY X 2 Y Sum Mean 8 121,57. untuk menghitung koefisien regresi dan intersep

26 Masukkan rumus b1 = XY {(X)(Y)}/n X 2 (X) 2 /n 8050 {(56)(851)}/7 = = 11, (56) 2 /7 Hitung nilai intersep bo = Y b1x = 121,57 (11,089) (8) = 32,857 Dapat juga dituliskan y = 11,089x + 32,857. Kemudian Gambarlah garis regresinya.

27 Wei ight (g) Garis Regresi Linier y = 11,089x + 32,857 R2 = 0, Age (days) Gambar garis regresinya

28 Hitung anova regresi JK Total = Y 2 (Y) 2 /n = (851) 2 /7 = 13951,71 JK regresi = b1 {XY (X)(Y)/n} = 11,089 x {8050 (56)(851)/7} = ,89 JK sisa = JK total JK regresi = 178,82 Setelah ketemu, masukkan dalam tabel anova regresi

29 ( Sumber keragaman Db JK KT F hit Regresi , ,89 385,15 ** Residu (sisa) 5 178,82 35,76 Total ,71 Koefisien Determinasi R 2 = JK Regresi/JK Total = 0,9872

30 Kesimpulan dan interpretasi Hubungan antara umur buah dengan bobot dapat dituliskan dengan persamaan regresi linier Y= 32, ,089X, artinya setiap penambahan umur satu hari, bobot buah akan bertambah 11,089 gram. Dari tabel anova dapat disimpulkan bahwa terdapat hubungan regresi yang sangat nyata antara umur buah dengan bobot buah berdasarkan regresi linier. Dari koefisien determinasi dapat disimpulkan bahwa sebanyak 98,72% keragaman berat buah disebabkan oleh pengaruh umur buah

31 Interpretasi : perhatikan persamaan ini./0,%(1-,+2 $** 3455 % 6 7./0,(%1"-,+#"%#/,, /0,(%1-,+2 792/"--0,(%#-,+/&-%0 : ;

32 Bahan Diskusi Untuk analisis regresi, carilah data independen dan dependen, cari persamaan regresinya, tunjukkan gambarnya, hitunglah anovanya, hitung koefisien determinasinya, dan berikan kesimpulannya