Exm4 - Prof John Kent PDF

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Prof John Kent...

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Math 3772 Exercises 4 This question is to be done in R. (a) Read in the cork data from the module web site (see Section 3.11 in the Lecture Notes) and represent the data in R as a matrix X (28 × 4). There are 4 variables, north, east, south and west. Using matrix operations (see Section 4.11), construct a new data matrix Y (28 × 3) with new variables, north + south - east - west, north - south east - west. (b) Compute the mean vectors and the variance and correlation matrices of X and Y . Using suitable plots, comment explicitly on each of the following issues: (i) the difference in mean bark thickness in the four directions (ii) the randomness of the data, (iii) the univariate normality of each variable, and (iv) the bivariate normality of each pair of variables. Hint: Some useful commands in R: cork=read.table("http://www1.maths.leeds.ac.uk/~john/3772/cork.txt", header=TRUE) # so cork is a data frame attach(cork) # vectors north, east, south, and west are now defined stem(north) # stem and leaf plot of a vector hist(north) # histogram of a vector boxplot(north, south, east, west) # boxplots of one or more vectors pairs(cork) # bivariate plot of the data corkm=as.matrix(cork) # corkm is a 28 by 4 data matrix matplot(corkm, col=1) # plot of each variable vs 1:n

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