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By Joyner D., Kreminski R., Turisco J.

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By Joyner D., Kreminski R., Turisco J.

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Example text

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.

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Applied Abstract Algebra by Joyner D., Kreminski R., Turisco J.


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