What is the appropriate back transformation for the convenient lambda

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Assignment #6

For each question, attach appropriate computer output for full points.

1. Refer to the SENIC data set in the previous assignments. We are interested in whether or not the mean length of stay (Y: LOS) is the same in the four geographic regions (Region).

a. Conduct a one-way ANOVA to compare the mean LOS among four regions. Write down the null and the alternative hypotheses. What is your conclusion based on the overall Ftest?

b. If the overall F-test is significant, then proceed to multiple comparisons using Tukey’s procedure. Report between which regions you find significant differences and corresponding Tukey’s adjusted p-values. Also, report the estimated means and their 95% confidence intervals. Produce a mean plot with error bars indicating the lower and upper confidence limits.

c. Fit an appropriate regression model to perform the same one-way ANOVA analysis that you did in part a) above. Use the reference coding and the reference group should be the West region (Region = 4). Write down the estimated regression equation. Make sure to give your interpretations of beta estimates.

d. Repeat the part c) above, but this time using the effect coding. Write down the estimated regression equation. Make sure to give your interpretations of beta estimates.

e. For the one-way ANOVA that you did in part a), obtain a plot of residuals against the predicted values, a normal probability plot, and a histogram of residuals. Also conduct the Brown-Forsythe test for homoscedasticity. What do you observe? Are ANOVA assumptions met?

f. Use the Box-Cox procedure to find an appropriate power transformation of Y. What is the value of the “convenient” lambda? What transformation should be applied?

g. Use the “convenient” lambda to apply an appropriate power transformation on Y. Conduct a one-way ANOVA on the transformed Y. If necessary, conduct Tukey’ multiple comparison procedure as well. Are the results same before and after the transformation? Comment.

h. Run ANOVA diagnostics, as you did in part e) above, on the transformed Y. Did the transformation help? What does the Brown-Forsythe test indicate? Are ANOVA assumptions met on the transformed Y? Comment.

i. What is the appropriate back-transformation for the “convenient” lambda? Backtransform estimated means of the transformed Y into the original scale. Make sure to apply the same back-transformation to the lower and upper confidence limits. Report the means for the four regions and their 95% confidence intervals in the original scale.

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