Stat 462 Final Exam Study Guide

      Note that this is a comprehensive final. Thus, in addition to reviewing the
      the study guides for the first two midterms, you should:


    * Be able to interpret the coefficients of a multiple regression
      model
    * Be able to determine the scope of the model in a multiple regression setting.
    * Understand and be able to interpret R-squared values and adjusted
      R-squared values.
    * Be able to define a linear regression model in matrix terms including assumptions.
    * Be able to define the fitted values and residuals in matrix terms.
    * Know how to multiply and add two matrices.
    * Be able to take the transpose of a matrix.
    * Know the definition of the inverse of a matrix.
    * Be able to read a scatter plot matrix and a correlation matrix.
    * Be able to calculate a confidence interval for a single slope.
    * Be able to interpret diagnostic plots in a multiple regression
      setting. (The only new ones we learned are "residuals against each
      predictor" and "residuals against omitted predictors.")
    * Know how the sequential sums of squares is a reduction in the
      error sum of squares or an increase in the regression sum of squares.
    * Be able to read (or in some cases, calculate) sequential sums of
      squares from Minitab output.
    * Be able to decompose a regression sum of squares into a sum of
      sequential sums of squares.
    * Be able to conduct a hypothesis test for a single slope being 0
      (using either a partial F test or a t-test).
    * Be able to conduct the overall F test for all of the slopes being 0.
    * Be able to conduct a partial F test for a subset of the slopes
      being 0 (more specifically be able to guess at the test statistic, derive
      the test statistic using general test approach and compute it using
      Minitab output for a given null about a subset of the slopes being 0).
    * Know how to specify the alternative hypotheses for each of the
      above tests (that is, know what it means if you reject the null
      for each of the above tests).
    * Know what multicollinearity means, and be able to recognize it in
      a scatter plot matrix or a correlation matrix.
    * Know the effect on regression analyses if the predictors are
      uncorrelated (similar slope estimates, regression sum of squares
      similar to sequential sum of squares)
    * Know the possible effects on regression analyses if the predictors
      are correlated (different slope estimates, regression sum of
      squares substantially different from sequential sum of squares,
      inflated standard errors of the coefficients, no problem with
      getting precise predictions of Y or estimations of mean, possibly
      different results for tests of individual slopes).
    * Know the general idea behind stepwise regression, and know how to read
      Minitab output of a stepwise regression procedure.
    * Know the general idea behind best subsets regression, and know how to
      read Minitab output of a best subsets regression procedure.
    * Know how to choose an optimal model based on R-square, adjusted R-square, 
      MSE, and the C-p criterion.
    * Know what it means to "center" the predictors and why and when we may use it.
    * Know that it is possible to "overfit" the data with polynomial models.
    * Understand why, in the presence of interactions, that we can't interpret slope coefficients like we previously did.