Topics 1/30 Lecture

1. Calibration problem, Section 7.4.4, Sleuth.
2. Simultaneous confidence intervals for slope and intercept parameters (Bonferroni), and for the mean response (Bonferroni, Working-Hotelling), simultaneous prediction intervals for a set of future observations (Bonferroni, Scheffe).
3. Application to example involving relationship between elemental carbon (Y) and mass (X) of diesel exhaust.
4. Transformations of X and Y. Diagnose using plots of residuals of regression.
   1. motivated by specific knowledge of problem at hand. Ease of interpretation.
   2. stabilize variance of dependent (Y) variable if homoscedasticity is violated. "horn-shape" residual pattern.
   3. normalize Y if normality assumption is violated.
   4. linearize the regression model, if the original data suggest a model nonlinear in either regression coefficients or original variables (dependent or independent).
5. Types: addition of quadratic term (used when residuals have a quadratic shape), log (transform Y or transform X and Y), square root (useful for data involving counts), reciprocal, arcsin (useful for proportions or rates), logit (useful for proportions; we'll see this in logistic regression).