# Homework Assignment for Lesson 7

### Homework Assignment

**1. Greenhouse Example**

Consider an experiment to study the effect of three types of fertilizer (F1, F2, and F3) on the growth of two species of plant (SppA and SppB). The data are found in the file greenhouse_hwk7.txt.

- Write out the 2-way complete model for this experiment.
- Fit the model using PROC MIXED in SAS and examine the residuals. Transform the response if needed to address any problems with normality or constant error variance. If you transform the response, clearly show the residuals from the un-transformed response, and your best transformation, and describe why you chose the transformation you did.
- Describe the effect of species and fertilizer on mean height. This description should use the results of hypothesis tests and p-values as described in class. Discuss any relevant interaction effects, main effects and pairwise differences between treatment means. Provide a plot that shows the means for all combinations of factor levels. Provide SAS code and output that supports your results.

**2. 2-factor Factorial Experiment**

Consider the following data (2factor_hwk7.txt), the result of a 2-factor factorial experiment with 5 replications for each combination of Factor A and Factor B. Treatment combinations were assigned at random to the 20 experimental units.

- Write out the 2-way complete model for this experiment.
- Fit the model using PROC MIXED in SAS and examine the residuals. Transform the response if needed to address any problems with normality or constant error variance. If you transform the response, clearly show the residuals from the un-transformed response, and your best transformation, and describe why you chose the transformation you did.
- Describe the effect of species and fertilizer on mean height. This description should use the results of hypothesis tests and p-values as described in class. Discuss any relevant interaction effects, main effects and pairwise differences between treatment means. Provide a plot that shows the means for all combinations of factor levels. Provide SAS code and output that supports your results.