Consider the following data of 11 samples on 8 variables by Anscombe, Francis J. (1973):

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	7.91
5	5	5	8	5.68	4.74	5.73

If the vector   and   then obtain the sample covariance matrix between x and y

Source: Anscombe, Francis J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17– 21. doi: 10.2307/2682899.

To obtain the sample covariance matrix between x and y, we first need to calculate the sample means of x and y, denoted as x̄ and ȳ, respectively. Then, we can calculate the deviations from the means for each observation (x_i - x̄) and (y_i - ȳ). Finally, we can compute the sample covariance using the formula:

cov(x, y) = Σ((x_i - x̄)(y_i - ȳ)) / (n - 1)

where n is the number of observations.

Given the data provided:

x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]
y = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]

First, we calculate the sample means:

x̄ = _____ ______ _______ _______ _______ ______.
__________ ______ ___ _____ ______ ___ _________.
__________ _______ _________ _____ __________ _________ ____ _____ _______ ___.
_______ _____ _________ ______ _______ _____ _______.
_____ ___ _______ ______ ________ ____ _____ _______ _______ ______ ______ ________.
____ _____ _________ _____ ___.
____ _____ _________ ______ ___ ____.
________ ____ ________ _____ _______ _______ ___ ____ ______ _____ ________.
__________ _________ ________ _______ ________.
___ ___ __________ ____ __________ _________ ________ ______ ____ ______.
___ ____ ______ _____ ____ ________ ______ _________ ___ _______ ____ ____.
___ _____ __________ ____ _________.
____ _________ ______ __________ __________ __________ ________ ____ ___.
__________ __________ _________ _____ _____ ________ _________ ___ __________ _______ _______ ______.
___ __________ ___ _______ ___ __________ _____ __________ _______ _______ ____ _________.
________ _____ ___ __________ ____ ________ ____ _________ ___ ____ _________.
_________ _______ _____ ____ ___ ___ ______ ______.
___ ______ ____ __________ __________ _________ _________ _______ _______.
_________ ______ _________ _______ ___ ____ ____ _____ ___ __________ _________ ______.
________ ________ _____ ________ _____ _____ ________ __________ ________ _______ ___.
_________ _________ ___ __________ __________ ______ _________ _____ ____ ___.
__________ _________ ________ _____ _____ ___ ________ ________ _____ ___.
__________ ___ ______ _________ ___ ______.
______ ________ ______ ____ ____ _______ _______ ________ _____.
_______ __________ ___ ______ _______ ________.
__________ __________ ___ ____ ____ ______ ________ _______ _______.
_____ ______ ______ ______ _______ ________ _______ _______ ____ ____ _________ ___.
____ _____ ______ ___ _____ ______ ____ ________ __________ ________.
_____ _______ ______ _______ ______ ___.
_________ ________ ______ ______ ________ _________ ______ _____ ________ ____ ______.
______ _________ ______ __________ _______ _____ _______.
___ _____ ______ ________ ______.
________ _________ ________ ___ ________ _______ _______ ___ __________ __________.
___ _______ _________ ________ _______ _________.
__________ _____ _______ _______ __________ ________.
_______ _____ _____ _____ ______ _________ __________ __________ _______ ________ _________.
____ _______ ___ __________ __________ ________ _______ _____ _____.
____ _______ ____ __________ ____ __________ __________ ______ ____ __________ ______ ________.
____ ________ _____ _________ ________ ___.
___ ___ ___ ________ ___.
Get Full Answer on WhatsApp