Design and and Analysis

STA 600
ASSIGNMENT 2 CHAPTER 3: DIAGNOSTICS AND REMEDIAL MEASURES
Diagnostic For Predicted Variable
Probems can occur when: * Outliers exist among X levels * X levels are associated with run order when experiment is run sequentially
Useful plots of X levels: * Dot plot for discrete data * Histogram /stem-and-leaf plot * Box plot * Sequence plot (versus time order)

Departures From Model To Be Studied By Residual 1. The regression function is not linear. 2. The error terms do not have constant variance. 3. The error terms are not independent. 4. The model fits all but one or few outliers, 5. The error terms are not normally distributed. 6. One or several important predictor(s) have been omitted from the model.

Diagnostic For Residuals
Six diagnostic plots to judge departure from the simple linear regression model * Plot of residuals against predictor variable. (The plot should have a random scatter of plots) * Plot of absolute or squared residuals against X. * Plot of residuals against the fitted values. * Plot of residuals against time or other sequence. (Should not display any trends) * Plots of residuals against omitted predictor variables. * Box plot of residuals. * Normal probability plot of residuals. (Should lie along a straight line)

EXAMPLE Predictor
Good Looking Plots

Figure: Normal probability plot Figure: Residual plot against predictor(x)

A. Nonlinearity * Plot of residuals against predictor variable * Plot of residuals against fitted values * Scatter plot How to detect: - look for systematic tendencies. - Random Cloud around 0 Linear Relation - U-Shape or Inverted U-Shape Nonlinear Relation

B. Nonconstancy of Error Variance * Plot of residuals against predictor