Question
Consider the following data of 11 samples on 8 variables by Anscombe, Francis J. (1973):
| x1 | x2 | x3 | x4 | y1 | y2 | y3 | y4 |
| 10 | 10 | 10 | 8 | 8.04 | 9.14 | 7.46 | 6.58 |
| 8 | 8 | 8 | 8 | 6.95 | 8.14 | 6.77 | 5.76 |
| 13 | 13 | 13 | 8 | 7.58 | 8.74 | 12.74 | 7.71 |
| 9 | 9 | 9 | 8 | 8.81 | 8.77 | 7.11 | 8.84 |
| 11 | 11 | 11 | 8 | 8.33 | 9.26 | 7.81 | 8.47 |
| 14 | 14 | 14 | 8 | 9.96 | 8.10 | 8.84 | 7.04 |
| 6 | 6 | 6 | 8 | 7.24 | 6.13 | 6.08 | 5.25 |
| 4 | 4 | 4 | 19 | 4.26 | 3.10 | 5.39 | 12.50 |
| 12 | 12 | 12 | 8 | 10.84 | 9.13 | 8.15 | 5.56 |
| 7 | 7 | 7 | 8 | 4.82 | 7.26 | 6.42 | 5.56 |
| 5 | 7 | 5 | 8 | 5.68 | 4.74 | 5.73 | 5.56 |
If the vectorthen obtain the sample covariance matrix between
Source: Anscombe, Francis J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17– 21. doi: 10.2307/2682899.
Answer :
Word Count : 510
We are asked to compute the sample covariance matrix between $\underline{x} = (x_1, x_2, x_3, x_4)^\top$ and $\underline{y} = (y_1, y_2, y_3, y_4)^\top$ for Anscombe's dataset. Let’s solve manually step by step. --- ### Step 1: Recall formula for covariance For two variables $X$ and $Y$ with $n$ observations: $$ \text{Cov}(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})(Y_i - \bar{Y}) $$ The sample covariance matrix between vectors $\underline{x} = (x_1, x_2, x_3, x_4)$ and $\underline{y} = (y_1, y_2, y_3, y_4)$ is a $4 \times 4$ _____ _______ __________ __________ ______ _____ __________.
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We are asked to compute the sample covariance matrix between $\underline{x} = (x_1, x_2, x_3, x_4)^\top$ and $\underline{y} = (y_1, y_2, y_3, y_4)^\top$ for Anscombe's dataset. Let’s solve manually step by step. --- ### Step 1: Recall formula for covariance For two variables $X$ and $Y$ with $n$ observations: $$ \text{Cov}(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})(Y_i - \bar{Y}) $$ The sample covariance matrix between vectors $\underline{x} = (x_1, x_2, x_3, x_4)$ and $\underline{y} = (y_1, y_2, y_3, y_4)$ is a $4 \times 4$ _____ _______ __________ __________ ______ _____ __________.
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Related Questions
Consider the following data of 11 samples on 8 variables by Anscombe, Francis J. (1973):
| x1 | x2 | x3 | x4 | y1 | y2 | y3 | y4 |
| 10 | 10 | 10 | 8 | 8.04 | 9.14 | 7.46 | 6.58 |
| 8 | 8 | 8 | 8 | 6.95 | 8.14 | 6.77 | 5.76 |
| 13 | 13 | 13 | 8 | 7.58 | 8.74 | 12.74 | 7.71 |
| 9 | 9 | 9 | 8 | 8.81 | 8.77 | 7.11 | 8.84 |
| 11 | 11 | 11 | 8 | 8.33 | 9.26 | 7.81 | 8.47 |
| 14 | 14 | 14 | 8 | 9.96 | 8.10 | 8.84 | 7.04 |
| 6 | 6 | 6 | 8 | 7.24 | 6.13 | 6.08 | 5.25 |
| 4 | 4 | 4 | 19 | 4.26 | 3.10 | 5.39 | 12.50 |
| 12 | 12 | 12 | 8 | 10.84 | 9.13 | 8.15 | 5.56 |
| 7 | 7 | 7 | 8 | 4.82 | 7.26 | 6.42 | 5.56 |
| 5 | 7 | 5 | 8 | 5.68 | 4.74 | 5.73 | 5.56 |
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