Problem 10. Verify by direct calculation that in the least squares analysis of a completely ran- domized design, essentially equivalent answers are obtained whatever admissible constraint is im- posed on the treatment parameters.

The model, y = Bo + B₁×1 + ß₂×₂ + ε, was fitted to a sample of 33 families in order to explain household milk consumption in quarts per week, y, from the weekly income in hundreds of dollars, X₁, and the family size, x2. The total sum of squares and regression sum of squares were found to be, SST = 162.1 and SSE(R) = 90.6. The least squares estimates of the regression parameters are bo = -0.022, b₁ = 0.051, and b₂ = 1.19. A third independent variable number of preschool children in the household-was added to the regression model. The sum of squared errors when this augmented model was estimated by least squares was found to be 83.1. Test the null hypothesis that, all other things being equal, the number of preschool children in the household does not affect milk consumption. Use α = 0.01. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. Choose the correct null and alternative hypotheses below. A. Ho: B3 = 0 |…

What is one of the optimal conditions for the non-linear programing problem Min z= x^2+3y^2+5z^2 subject to x+y=2 and y+z=1?

4. Given the following data, do a quadratic least squares polynomial fit using P2(r) = ao + a1r + azx?. Yi Yi Yi -1.0 7.904 -0.3 0.335 0.4 -0.711 0.224 0.689 -0.9 7.452 -0.2 -0.271 0.5 -0.8 5.827 -0.1 -0.963 0.6 0.7 -0.7 4.400 -0.847 0.861 -0.6 2.908 0.1 -1.278 0.8 1.358 -0.5 2.144 0.2 -1.335 0.9 2.613 -0.4 0.581 0.3 -0.656 1.0 4.599