By Joyner D., Kreminski R., Turisco J.
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2. 99 3 2 x2 3 5 4 (a) Construct a scatter plot of the data and marginal dot diagrams. (b) Infer the sign of the sample· covariance s 12 from the scatter plot. (c) Compute the sample means :X 1 and :X 2 and the sarilple variances s 11 and Szz. Compute the sample covariance s 12 and the sample correlation coefficient r12 . Interpret these quantities. (d) Display the sample mean array x, the sample variance-covariance array Sn, and the sample correlation array R using (1-8). 3. The following are five measurements on the variables x 1 , x 2 , and x 3 : X1 9 2 6 5 8 x2 12 8 6 4 10 x3 3 4 0 2 1 Find the arrays i, S", and R.
Bear2 Bear! J 140 3 4 Year 180 -5 ff 160 j 140 5 / 2 3 4 Year 5 Bear? 1 S Individual growth curves for length for female grizzly bears. 5 • We now turn to two popular pictorial representations of multivariate data in two dimensions: stars and Chernoff faces. Stars Suppose each data unit consists of nonnegative observations on p ~ 2 variables. In two dimensions, we can construct circles of a fixed (reference) radius with p equally spaced rays emanating from the center of the circle. The lengths of the rays represent the values of the variables.
Notice that the records for the 800-m, 1500-m, 3000-m and marathon runs are measured in minutes. 2 miles, or 42,195 meters, long. Compute the x, Sn, and R arrays. Notice the magnitudes of the correlation coefficients as you go from the shorter (100m) to the longer (marathon) running distances. Interpret these pairwise correlations. 17. 19. 9.
Applied Abstract Algebra by Joyner D., Kreminski R., Turisco J.