Слайд 2
![Experimental Setting 2-Way ANOVA with one measurement per combination of](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/286063/slide-1.jpg)
Experimental Setting
2-Way ANOVA with one measurement per combination of levels of
factors A and B (N=a(b)(1))
Additive Model: E(Yij)= μ + αi + βj
Interaction Model (1 df): E(Yij)= μ + αi + βj + αβij
Where αβij = ηαiβj/μ = Dαiβj
Procedure Involves Estimating D and testing whether the parameter equals 0
Слайд 3
![Data – 18 Years for 8 Business Indices Factor A: Year (a=18) Factor B: Index (b=8)](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/286063/slide-2.jpg)
Data – 18 Years for 8 Business Indices
Factor A: Year (a=18)
Factor B: Index (b=8)
Слайд 4
![Algorithm Fit the additive Model and estimate μ, αi and](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/286063/slide-3.jpg)
Algorithm
Fit the additive Model and estimate μ, αi and βj
Fit
the interaction model with αβij = Dαiβj
Use Least Squares to estimate D
Obtain Sum of Squares for Interaction and Remainder
Conduct 1-degree of freedom F-test of H0: D=0
Слайд 5
![OLS Estimation of D](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/286063/slide-4.jpg)
Слайд 6
![Sum of Squares for Interaction (αβij = Dαiβj )](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/286063/slide-5.jpg)
Sum of Squares for Interaction (αβij = Dαiβj )
Слайд 7
![Business Index Example Y](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/286063/slide-6.jpg)
Слайд 8
![Sums of Squares & F-Test for Interaction](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/286063/slide-7.jpg)
Sums of Squares & F-Test for Interaction