Question

how is a linear relationship between two variables measured in statistics? explain.
select all the true statements.
there are several numerical measures of correlation, called correlation coefficients.
the correlation coefficient ranges from - 1 to 1. values closer to 0 show a strong linear relationship.
the correlation coefficient ranges from - 1 to 1. values close to + 1 or - 1 show a strong linear relationship.
if the values of x and y are interchanged, the correlation coefficient remains the same.
the value of the coefficient is resistant to outliers.

Explanation:

1. There are multiple correlation - coefficients to measure linear relationships, so the first statement is true.
2. The correlation coefficient ranges from - 1 to 1, but values close to 0 indicate a weak linear relationship, not a strong one. So the second statement is false.
3. Values close to + 1 or - 1 in the range of the correlation coefficient from - 1 to 1 show a strong linear relationship, so the third statement is true.
4. The correlation coefficient is symmetric with respect to the two variables. Interchanging x and y does not change its value, so the fourth statement is true.
5. The correlation coefficient is not resistant to outliers. Outliers can greatly affect its value. So the fifth statement is false.

Answer:

There are several numerical measures of correlation, called correlation coefficients.
The correlation coefficient ranges from - 1 to 1. Values close to + 1 or - 1 show a strong linear relationship.
If the values of x and y are interchanged, the correlation coefficient remains the same.