Determine the value of correlation coefficient from the following… - Vidyadip

Question

Determine the value of correlation coefficient from the following data:
$(1)\ \sum (x – x̄)^2 = 72, \sum (y – ȳ)^2 = 32,$
$\sum (x – x̄) (y – ȳ) = 45$
$(2)\ n = 6, \sum x = 16, \sum y = 51, \sum xy = 154,$
$\sum x^2 = 52, \sum y^2 = 471$

✓

Answer

$(1)$ Here, $\sum (x – x̄)^2 = 72; \sum (y – ȳ)^2 = 32$ and $Σ(x – x̄) (y – ȳ) = 45.$
$= \frac{\Sigma(x-\bar{x})(y-\bar{y})}{\sqrt{\Sigma(x-\bar{x})^{2}} \cdot \sqrt{\Sigma(y-\bar{y})^{2}}}$
$= \frac{45}{\sqrt{72} \times \sqrt{32}}$
$= \frac{45}{\sqrt{2304}}$
$= \frac{45}{48}$
$= 0.94$
Hence, the correlation coefficient obtained is $0.94.$
$(2)\ \sum x^2 = 52, \sum y^2 = 471$
Here, $n = 6; \sum x = 16; \sum y = 51; \sum xy = 154; \sum x^2 = 52$ and $\sum y^2 = 471.$

Hence, the correlation coefficient obtained is $0.96.$

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