STA442/1008 Assignment 9

Quiz in Tutorial on Friday March 23d

  1. Suppose you have a data set with a quantitative dependent variable Y, quantitative independent variables X1 and X2, and factors A, B and C. Factor A has 3 levels (categories), factor B has 2 levels and factor C has 3 levels. You see this SAS code; 
                    proc glm;
                class A B C;
                model Y = X1 X2 A|B|C;
    1. Is this an analysis of covariance? Answer Yes or No. If Yes, what are the covariates?
    2. Indicate how you would define dummy variables for the factors, using effect coding. Use names like a1, a2, and so on.
    3. Write E(Y|X=x) for a regression model equivalent to the proc glm model above.
    4. For the initial F-test produced by proc glm,
      1. State the null hypothesis in terms of β quantities from your regression model.
      2. How many (numerator) degrees of freedom will be in your test?
    5. For each of the following effects in the proc glm model, state the null hypothesis in terms of β quantities from your regression model. You need not show any work. Just write down the answers.
      1. Main effect of A.
      2. Main effect of B.
      3. Main effect of C.
      4. A by B interaction.
      5. A by C interaction.
      6. B by C interaction.
      7. A by B by C interaction.
    6. Controlling for the covariates, are there any differences among the 18 treatment means? State the null hypothesis you would test in order to answer this question. You answer should be in terms of β quantities from your regression model.

  2. Please revisit the infamous bunny data. Do a two-way multivariate analysis of variance, with time and drug as the independent variables, and force and stiffness as the dependent variables. Conduct tests for the following. In each case, do it the easiest way you can.
    1. Main effect of Drug
    2. Main effect of Time
    3. Drug by Time interaction
    4. Effect of Drug just at day 12.

    Of course you need to look at sample means as well as just doing the tests. Following up any significant multivariate tests with the corresponding univariate tests using a Bonferroni correction, what do you conclude? Note that this assignment is asking for a lot less detail than Assignment 8 did, so you can just cut out a lot of material when you edit (a copy of) your SAS program. Also, you do not need to follow up significant univariate tests for the main effect of time with pairwise comparisons of marginal means (though you could). Just be ready to describe any trends in plain language.

  3. In a taste test of wine, 6 professional judges judged 4 wines. The numbers they gave do not exactly represent quality. Instead, they are maximum prices in dollars per bottle that the judge thinks the company can charge and still sell most of the wine. I suppose we are assuming that the 6 judges are some kind of random sample, even though they probably are not. The data are available in the file Wine.data.

    We want to know if there are any average differences among the wines in how expensive the judges think they should be. If so, we want to know which wines are potentially more expensive than which other wines. Carry out the appropriate analysis, with Bonferroni-corrected pairwse comparisons if the initial test is significant. Be ready to state your findings in plain, non-statistical language.

 

Please bring both sets of log and list files to the quiz. As usual, answers to the questions are not to be handed in. They are just practice for the quiz. Please do not write anything on your printouts except your name and student number. Of course for each job, the log and list files must be from the same run of SAS or marks will be deducted.