Question

Use the above data to calculate the correlation coefficient Answer Choices.0.890.94-0.89-0.94

Answer 1

Using the table, we have the following points:

(x1, y1) ==> (2.5, 3), (3.5, 4.5), (5, 4.8), (5.5, 5.2), (6, 5.5)

Let's find the correlation coefficient.

To find the correlation coefficient, apply the formula:

`r=(n\Sigma xy-\Sigma x\Sigma y)/(√((n\Sigma x^2-\Sigma(x)^2)(n)\Sigma y^2-\Sigma(y)^2))`

Where:

n = 5

Σx = 2.5 + 3.5 + 5 + 5.5 + 6 = 22.5

Σy = 3 + 4.5 + 4.8 + 5.2 + 5.5 = 23

Σxy = 2.5⋅3 + 3.5⋅4.5 + 5⋅4.8 + 5.5⋅5.2 + 6⋅5.5 = 108.85

Σx² = 2.5² + 3.5² + 5² + 5.5² + 6² = 109.75

Σy² = 109.6

Plug in values in the formula and solve for r.

We have:

`\begin{gathered} r=(5(108.85)-(22.5)(23))/(√((5(109.75)-22.5^2)(5(109.6)-(23)^2)) \\ \\ r=0.94 \end{gathered}`

Therefore, the coefficient is 0.94

ANSWER:

0.94