Get the answer to "Find the covariance sxy using bivariate data."

College
Statistics and Probability
College Statistics
Bivariate numerical data

lwfrgin

Answered question

2021-01-04

Find the covariance

s_{x y}

using bivariate data.

Answer & Explanation

Macsen Nixon

Skilled2021-01-05Added 117 answers

The given bivariate data is(1,6),(3,2),and(2,4).
Calculation:
First determine $\sum x_{i} y_{i}, \sum x_{i} and \sum y_{i}$ .
$x_{i} \to$ first coordinates of the ordered pairs.
$y_{i} \to$ second coordinates of the ordered pairs.
$\sum x_{i} y_{i} = 1 \cdot 6 + 3 \cdot 2 + 2 \cdot 4 = 20$
$\sum x_{i} = 1 + 3 + 2 = 6$
$\sum y_{i} = 6 + 2 + 4 = 12$
For covariance $s_{x y} u s i n g f or μ s_{x y} = \frac{\sum x_{i} y_{i} - \frac{\sum x_{i} - \sum y_{i}}{n}}{n - 1}$ .
Where n = number of ordered pairs.
n=3
$s_{x y} = \frac{20 - \frac{6 \cdot 12}{3}}{3 - 1}$
$= \frac{20 - \frac{72}{3}}{3 - 1}$
$= \frac{2 - 24}{2}$
$= - \frac{4}{2} = - 2$
Hence $s_{x y} = - 2$ .

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