Question

what is the correlation coefficient of the following data? is it a strong or weak correlation? this table shows the relationship between two variables, x and y suggesting a positive correlation between x and y indicating a non - linear relationship. x 1 3 5 7 9 y 13 43 51 76 81 (1 point) 0.97300135, weak 0.97300135, strong - 0.97300135, weak - 0.97300135, strong

Explanation:

Step1: List given data pairs

Data: $(1,13), (3,43), (5,51), (7,76), (9,81)$; $n=5$

Step2: Calculate sum values

First, compute required sums:
$\sum x = 1+3+5+7+9 = 25$
$\sum y = 13+43+51+76+81 = 264$
$\sum xy = (1×13)+(3×43)+(5×51)+(7×76)+(9×81) = 13+129+255+532+729 = 1658$
$\sum x^2 = 1^2+3^2+5^2+7^2+9^2 = 1+9+25+49+81 = 165$
$\sum y^2 = 13^2+43^2+51^2+76^2+81^2 = 169+1849+2601+5776+6561 = 16956$

Step3: Apply correlation formula

Use Pearson correlation coefficient formula:
$$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$$
Substitute values:
$$r = \frac{5×1658 - 25×264}{\sqrt{[5×165 - 25^2][5×16956 - 264^2]}}$$
$$r = \frac{8290 - 6600}{\sqrt{[825 - 625][84780 - 69696]}}$$
$$r = \frac{1690}{\sqrt{[200][15084]}}$$
$$r = \frac{1690}{\sqrt{3016800}} = \frac{1690}{1736.8938} ≈ 0.97300135$$

Step4: Classify correlation strength

A correlation coefficient close to 1 (absolute value > 0.7) is strong positive correlation.

Answer:

0.97300135; strong