STA442/1008 Assignment 7

Quiz in tutorial on Friday March 14th

1. One thing we don't know about the Furnace data is whether the two different types of vent damper tend to be installed in houses that differ systematically in ways that might be connected to energy consumption (this would be a problem). To partly examine this issue, do a multivariate analysis in which the independent variable is type of vent damper, and the dependent variables are chimney area, chimney height, and age. For age, ignore the fact that 99 = 99+. If the multivariate test is significant, treat the univariate tests as Bonferroni-protected follow-ups. Okay, that was reassuring.
2. Now still with the furnace data, do a multivariate analysis in which the independent variable is type of vent damper, and the dependent variables are energy consumption with the damper active and energy consumption with the damper inactive. If the multivariate test is significant, treat the univariate tests as Bonferroni-protected follow-ups. Again if the results are statistically significant, state the conclusions in plain, non-statistical language. If the results are not significant, you would write something like "There is no evidence that energy consumption is connected to type of vent damper."
3. The salmon.data represent growth for a sample of Alaskan and Canadian salmon. Apparently, growth during different time periods can be estimated by the diameter of rings in a fish's scales. We have two measurements of growth: marine growth (growth during the fishes' first year of life in the ocean) and freshwater growth. The variables are:
   • country 1=Alaskan 2=Canadian
   • gender 1=Female 2=Male
   • fresh Diameter of rings for first-year freshwater growth in 100ths of an inch
   • marine Diameter of rings for first-year marine growth in 100ths of an inch
   Now carry out a two-factor multivariate analysis of variance in which the independent variables are gender and country of origin, and the dependent variables are freshwater growth and marine growth. Follow up any significant multivariate tests with Bonferroni-corrected univariate tests, and of course look at the cell means. What do you conclude (in plain language)?