Question

Which is most likely the correlation coefficient for the set of data shown?


A.–0.83

B.–0.21

C.0.21

D.0.83

Answer 1

we know that

The correlation coefficient is a number between $-1$ and $+1$ that represent the linear dependence of two variables or sets of data

Let

$A(1,4)\ B(2,1.5)\ C(3,3)\ D(4,4)\ E(5,2)$

Using the function CORREL in a Excel tool

Find the correlation coefficient for the set of data

see the attached table

the correlation coefficient is  $r=-0.20801$

therefore

the answer is the option B

$-0.21$

Answer 2

You can use the Pearson's correlation coefficient formula to calculate the correlation coefficient for given set of data.

The correlation coefficient for the given set of data is given by

Option B: -0.21

How can we calculate the Pearson's correlation coefficient from the coordinates of data point?

The correlation coefficient(denoted by r) for given data points can be calculated as:

$r = \dfrac{\sum (x_i - \overline{x})(y_i - \overline{y})}{\sqrt{\sum (x_i - \overline{x})^2\sum (y_i - \overline{y})^2}}$

where

$(x_i, y_i) = \text{data points' coordinates}\\\overline{x} = \text{mean of values of x variables}\\\overline{y} = \text{mean of values of y variables}$

Using above formula for given data points,

$(x_1, y_1) = (1,4)\\(x_2, y_2) = (2,1.5)\\(x_3, y_3) = (3,3)\\(x_4, y_4) = (4,4)\\(x_5, y_5) = (5,2)$

The mean of x values is (1+2+3+4+5)/5 = 3

Similarly, mean of y values is 2.9

Putting in the formula, we get:

r = -1.5 / √((10)(5.2)) = -0.208

Thus,

The correlation coefficient for the given set of data is given by

Option B: -0.21

Learn more about correlation coefficient here:

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