STA 6167 – Project 2

Regression Diagnostics, CRD, RBD, and 2-Way ANOVA

Part 1: Stature, Hand Length, Foot Length, and Gender

Dataset: stature_hand_foot.dat

Source: S.G. Sani, E.D. Kizilkanat, N. Boyan, et al. (2005)."Stature Estmation Based on Hand Length and Foot Length," ClinicalAnatomy, Vol. 18, pp. 589-596.

Description: Stature, hand length, and foot length among 80 males and 75 females.

Data simulated to have equal means, SDs, and correlations.

Variables/Columns

ID (w/in gender) 7-8

gender 16 /* 1=M, 2=F */

Stature (height, mm) 18-24

Hand length (mm) 26-32

Foot length (mm) 34-40

Fit a regression model, relating Stature to Hand Length, Foot Length and Female Indicator (Gender-1). Include interactions and quadratics in Hand and Foot Length.

  1. Select a parsimonious model based on minimizing AIC (this may be the Complete Model).
  2. Obtain a Plot of Residuals versus Fitted Values. Does the constant variance assumption seem reasonable?
  3. Obtain a Normal Probability Plot for the residuals. Does the Normality assumptionappear to be reasonable?
  4. Conduct the Shapiro-Wilk Test for testing H0: Errors are Normally Distributed.
  5. Conduct the Breusch-Pagan Test for testing H0: Errors have Constant Variance

Part 2: Water Evaporation in the Growing Season in India

Dataset: h2o_evap.dat

Source: A. Krishnan and R.S. Kushwaha (1973). "A Multiple Regression Analysisof Evaporation During the Growing Season of Vegetation in the Arid Zone ofIndia," Agricultural Meteorology, Vol. 12, pp. 297-307

Description: Factors related to Evaporation (mm/day) for 49 5-day periods

in 1963-1964. Predictors: total global radiation (X1, cal/cm^2/day),

estimated net radiation (X2, cal/cm^2/day), saturation deficit at max temp

(X3, mm of Hg), mean daily wind speed (X4 km/hour) and saturation deficit

at mean temp (X5, mm of Hg). Models fit: Y=X1,X3,X4 and Y=X2,X3,X4

Variables/Columns

Period 7-8

Evaporation 10-16

total global radiation 18-24

net radiation 26-32

saturation deficit at max temp 34-40

wind speed 42-48

saturation deficit at mean temp 50-56

Fit the model relating Evaporation to Total global radiation, Saturation deficit at max temp, and wind speed.

  1. See whether a Box-Cox Transformation on Evaporation improves Normality
  2. If necessary, transform Evaporation, and re-fit the model.
  3. Conduct the Durbin-Watson Test, to test H0: Errors are independent.
  4. Obtain Estimated Generalized Least Squares estimates of the Regression Coefficients, and t-tests.

Part 3: Mollusc Nervous Impulse Reactions

A study compared nervous impulse measurements (cm/sec) for 5 species of molluscs. Complete the following parts (note the large differences in variation in part A, and use ln(impulse) in subsequent parts:

  1. Plot the measurements versus species and note the differences in variation among species.
  2. Obtain means and standard deviations for the 5 species, as well as across species.
  3. Obtain the Analysis of Variance, and test whether the population means differ among the 5 species at the 0.05 significance level.
  4. Use Tukey’s and Bonferroni’s methods to compare all pairs of species with an experimentwise error rate of E = 0.05
  5. Use the Kruskal-Wallis test to test whether the population means (medians) differ at the 0.05 significance level.

Part 4: Pharmacokinetics of Flurbiprofen

  1. Run the Analysis for Problem 37 in the Course Notes (F-test for RBD)
  2. Run the Analysis for Problem 38 in the Course Notes (Friedman’s test for RBD)

Part 5: Comparison of 3 Formulations of 2 Brands of Suntan Lotion

  1. Obtain means and standard deviations for all combinations of brand and formulation. The response measures the total color change for the specimen.
  2. Obtain the Analysis of Variance
  3. Test for a Brand by formulation interaction at 0.05 significance level
  4. If appropriate, test for Main effects among brands and formulations
  5. By hand or spreadsheet, compare all pairs of formulations separately by brand using Bonferroni’s method with E = 0.05.