ANCOVA It is known that increased reproductions leads to reduced longevity for femaie fruitflies. Patridge and Farquhar (1981) studied whether the same phenomenon held for male fruitflies. The experiment set up ve treatment groups, each consisting of 25 randomly assigned male fruitflies. The males in one treatment were housed with eight virgin females per day. In another treatment, the maies were housed with one virgin female day. There were three control groups: males housed with eight newly impregnated females, housed with one newly impregnated femaie, and housed alone. (Newly inseminated females will not usually mate within two days). It is also believed that the males' thorax length at birth has a correlation with its lifespan. Treatments: 8 virgin female fruitflies, 1 virgin female fruitflies, 8 pregnant female fruitflies, 1 pregnant female fruitfiies and \"none\" (housed alone). Response: Longevity (lifespan in days). Covariate: Thorax length of male fruitflies at birth (in mm). Questions: 1. Obtain side-by-side boxplots of the lifespan against the treatments. Do a one-way anova (ignoring the covariate effect) and test for a difference among the treatments. Compute the s.e. of the pairwise treatment differences. [You'll later see that including the covariate effect greatly reduce these se's and can detect treatment differences]. 2. Obtain a scatterplot of the lifespan against the thorax lengths at birth for every treatment. 3. Was thorax length at birth balanced across the treatments? Explain. To answer this question, obtain side-byside boxplots of thorax length at birth