STAT 4504: CRD Experiment with a Single Explanatory Variable - Statistics Assignment Help

Assignment Task:

Use SAS to help answer the following questions. Hand in a copy of BOTH code and output. (minus the actual data set). 

Remember to put a FOOTNOTE statement with your name and student number at the beginning of your program.

a) Assuming fixed factor levels, give the complete cell means the model specification for this experiment. 
b) Use PROC UNIVARIATE to obtain side-by-side box plots for the factor levels. State which factor levels, if any, have outliers and which have extreme outliers. 
c) Have the fitted value, median standard deviation, and variance for each factor level printed out.  
d) Plot the residuals vs the fitted values. 
e) What is indicated by this residual plot? Do the box-plot confirm this information? Why or why not? 
f) Use the Brown-Forsythe test to test for inequality of treatment variances. Use α = .10. Are your results consistent with your diagnosis in part (e)? 
g) Obtain normal probability plots of the residuals for each treatment (factor level). Do there seem to be any obvious violations of the normality assumptions? Explain. 
h) For each treatment, obtain the correlation coefficient between the ordered residuals and the expected values under normality. Use this to test whether there evidence of non-normality? Use α = .05. (Tables to be handed out in class). Are your conclusions here consistent with your answer in (g)? 
i) Prepare residual sequence plots. What are your conclusions? 
j) For each winding speed, use the factor level means, variances & standard deviations printed out in (c) to check the possibilities of the variance stabilizing transformations 1/Y, ln(Y), SQRT(Y), and determine the transformation that would be most appropriate. Explain why you chose this transformation. Do by hand (or Excel and show your work. 

3. Using the transformation you chose in 2(j) 

a) Give the new model for the transformed data. 
b) Obtain side-by-side box plots for the factor levels. Do these show any obvious outliers? 
c) For each factor level, have the fitted value and the standard deviation printed out. Are the standard deviations now fairly similar for all winding speeds? 
d) Plot the residuals vs the fitted values. What is indicated by this plot? 
e) Use the Brown-Forsythe test to test for inequality of treatment variances. Use α = ..10. What is the p-value of the test? Are your results consistent with your diagnosis in part (d)? 
f) Obtain normal probability plots of the residuals for each treatment (factor level). Do there seem to be any obvious violations of the normality assumptions? Explain. 
g) For each treatment, obtain the correlation coefficient between the ordered residuals and their expected values under normality. Use these correlation coefficients to check whether there is evidence of non-normality? Use α = .05. 
h) If appropriate, test for equality of factor level means. Use α = .05 When would it not be appropriate?
i) Obtain the Tukey confidence intervals for all pairwise comparisons between factor level means for your transformed variable. Use a 95% confidence coefficient. Interpret your results in the words of the problem.

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