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The following n\times p data matrix contains n=3 observations for each of p=2 variables x_(1) (column 1) and x_(2) (column 2). [[3,18],[8,21],[4,20]] Calculate each of the following. You can check your work with software, but you should show by hand how the numbers in this case fit into the formula for each. (a) The sample mean vector \bar{x} Hint: this is a 2\times 1 vector consisting of the sample means for both variables (b) The sample covariance matrix S. Note that we divide by n-1n 2\times 2 matrix consisting of the sample variances for both variables on the diagonals and their covariance on the off-diagonals (c) The sample correlation matrix R

          The following n\times p data matrix contains n=3 observations for each of p=2 variables x_(1) (column 1) and x_(2) (column 2). [[3,18],[8,21],[4,20]] Calculate each of the following. You can check your work with software, but you should show by hand how the numbers in this case fit into the formula for each. (a) The sample mean vector \bar{x} Hint: this is a 2\times 1 vector consisting of the sample means for both variables (b) The sample covariance matrix S. Note that we divide by n-1n 2\times 2 matrix consisting of the sample variances for both variables on the diagonals and their covariance on the off-diagonals (c) The sample correlation matrix R

the following ntimes p data matrix contains n3 observations for each of p2 variables x1 column 1 and x2 column 2 318821420 calculate each of the following you can check your work with soft 08142

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