Question

Which is most likely the correlation coefficient for the set of data shown? –0. 83 –0. 21 0. 21 0. 83.

Answer 1

A correlation coefficient suggest that how well the line of data best fits in the data set.

The the correlation coefficient for the set of data shown is -0.21

What is the correlation coefficient?

Correlation coefficient is used to calculate that how strong the relationship is between the two variables.

A correlation coefficient suggest that how well the line of data best fits in the data set.

The more the value of the correlation coefficient (between +1 to -1), the better the line fits in the data set.

• When the correlation coefficient is positive, then the data set is in the increasing order.

• When the correlation coefficient is negative, then the data set is in the decreasing order.

The value of the correlation coefficient must be between 1 to -1 otherwise the error in the correlation coefficient occurs, when finding its value.

Given information-

The data set given in the problem is,

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

The formula to find correlation coefficient is,

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

Here, $x_i, y_i$values of the $x$ and $y$ variables in the sample and $\overline x, \overline y$ is the mean of the x and y variables.

Put the values from the data set, we get,

$r=-0.2081$

Hence the the correlation coefficient for the set of data shown is -0.21

Learn more about the correlation coefficient here;

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