Question

Which of the following are properties of the linear correlation​ coefficient?

a. If r is close to​ 0, then little or no evidence of any relation between the explanatory or response variable exists.
b. The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.
c.The correlation coefficient is resistant.
d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.
e. A linear correlation of 0.639 suggests a stronger linear relation between two variables than a linear correlation of −0.639.
f. If r=−​1, then a perfect negative linear relation exists between the two variables.

Answer 1

Among the options given in the question, the following are the properties of the linear correlation coefficient:

The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

If r=−​1, then a perfect negative linear relation exists between the two variables.

Properties of linear correlation coefficient:

Linear correlation coefficient is a value calculated from given data and used to measure the strength of linear relationship between two variables, for instant between x and y variables.

The sign of this coefficient (r) indicates the direction linear relationship will take between x and y. Below are some properties of the linear correlation coefficient:

• The value of r lies between -1 and 1 inclusive
• The sign of r indicates the direction of the linear relationship between x and y
• The size of r indicates the strength of the linear relationship between x and y

Now, the properties of the linear correlation coefficient among the given ones in the question are:

b. The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

f. If r=−​1, then a perfect negative linear relation exists between the two variables.

Hence, options b, d and f are correct.

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