Determine number of significant canonical dimension

Assignment Help Applied Statistics

Reference no: EM132502520

Multivariate Assignment - Need this done in R markdown.

Problem 1 - The data set ChiMarathonMen contains data on a sample of the men, ages between 20 and 39 years, who completed the Chicago Marathon in 2015. The runners were classified into age groups, 20-24, 25-29, 30-34, and 34-39. Their finishing times are given in minutes.

(i) Conduct an appropriate test to see if the mean finishing times are the same across age groups. Justify your method.

(ii) Is the equal-variance assumption satisfied? HINT: Use the testequavar package, 5% significance level and 5000 bootstrap samples. Make sure you declare your input column using as.vector().

Problem 2 - Let x = (x₁ x₂ x₃)' follow a multivariate normal distribution with μ = E(x) = (1 2 3)' and

Let x* = (x₁ x₃)'. Find

(i) CORR(x*), i.e., the correlation matrix for x*;

(ii) Conditional density of x*|x₂ = 1.

Problem 3 - Consider the car (mtcars) data.

(i) Determine the appropriate number of significant canonical dimension or pairs. Interpret the first two loadings for the driver features.

(ii) Perform a principal components analysis using the correlation for the driver features. How many PC's are sufficient? What is the proportion of the total variance that is explained by the sufficient PCs? Are the first two loadings comparable to those of the canonical correlations in part (i)?

(iii) Using comput from CCA package appropriately for the (mtcars) data. The correlations between observed variables and canonical variables are called as the canonical loadings. What is the correlation between disp and the first 'driver' canonical variates? What is the correlation between hp and the first 'design' canonical variates? What is the correlation between the first 'driver' canonical variates and the second 'design' canonical variates?

Reference no: EM132502520

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