Please use the Chapters 8, 9, and 10 (from page 430 to page 574) of Johnson and Wichern (in the sixth
edition) (http://www.udel.edu/oiss/pdf/617.pdf)
Question 1:- Consider the Mali family farm data discussed in problem 8.28 (in Table 8.7 in the sixth edition) (page.479)
(a) Determine the value of the sample variance and the sample correlation matrices of the data provided.
(b) Which one, the sample variance covariance matrix (S) or sample correlation matrix (R) to conduct the principle components analysis for the data provided? Explain the reasons why you choose S or R.
(c) For your chosen matrix,
-Produce a table that shows the proportion of the total variability accounted for by each eigenvalue.
-Produce a scree plot of this information.
How many dimensions do you think are required to summarize these data? Explain your rationale.
(d)Give all of the principal components in a table along with the corresponding eigenvalue. Provide an interpretation of the coefficients of the first two principal components in words.
(e) Draw a Q-Q plot of the first two principal components. How would you summarize these plots?
(f) Draw a scatterplot of the first two scores vectors that you get when applying the principal component loadings to each of the data values in turn (you may refer to Ex 8.7 on page 454), and comment.
(g) Write a summary of what you have done in the above analysis. Try to use simple English without any statistical jargon assuming that you are reporting your analysis to persons who do not know statistics.
Question 2:-
(a) Using the sample correlation matrix to perform a factor analysis of these data.
(b) Choose the value of m (common factors) and justify why you choose that m and the method of extraction.
(c) Do you think that it is helpful to rotate the data? Try 2 methods of rotate and decide if you should rotate or not.
If you decide to rotate, give the corresponding rotation matrix. Try to interpret the factors that you get.
(d) Try to draw some appropriate plots to support your analysis.
(e) Write a summary of what you have done in the above analysis. Try to use simple English without any statistical
jargon assuming that you are reporting your analysis to persons who do not know statistics.
Question 3:- Consider the pulp and paper data set described in Exercise 7.26 (and Table 7.7). (page.426). It is of interest to
establish a relation between the four paper variables and the four pulp variables.
(a) Provide the sample canonical variates and their corresponding correlations. Try to interpret these values as clear as possible.
(b) Explain why or why not that the first canonical variates are good summary measures of their respective sets of variables. Justify your answers with a clear explanation.
(c) Perform a significance test of the canonical relations using α = 0.05.
(d) Write a summary of what you have done in the above analysis. Try to use simple English without any statistical jargon assuming that you are reporting your analysis to persons who do not know statistics.
Attachment:- Assignment.rar