Homework #2 STAT 506 Spring 2013

1. Refer back to HW2 of Stat 505. Reanalyze the same data in SAS.
   Researchers in Jordan are interested in plants useable for animal fodder which require little moisture. They tested four plant species in a greenhouse experiment varying the daily watering from 50 to 650 mm in 100 mm increments. Within each species, water amounts were allocated at random. The response is dry biomass. Read in the data from here .
   1. Plot the data in a manner which allows us to easily compare median biomass for each species as a function of water.
   2. Fit a model with an intercept and a slope for each plant.
      y_i = β₀ + β₁ x_i + α _0j[i] + α _1j[i] x_i + ε_i
      In this notation, i is the row number, j[i] is the plant species of the plant in row i (j = 1 to 4), β's are overall effects, and α's are adjustments for each plant species.
      1. Fit this model in SAS and show the estimated coefficients.
      2. Provide either the Type I or Type III output table, and explain why you think this table is preferred. Is the interaction needed?
      3. What combination of Greek letters is estimated by each coefficient shown?
      4. Plot the four lines from the interaction model.
      5. Provide the default diagnostic plots and comment on how well the assumptions are met.
2. Refer back to HW4 of Stat 505. Reanalyze the warpbreaks data in SAS. Provide estimates of the effects of tension and wool type
   
   1. Using a transformation on the response.
   2. Using appropriate weights, which could come from the R models we ran last semester.
   Provide suitable diagnostic plots for each.
   Summarize your findings.

 

    
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