Question

two quantities of data have a strong positive correlation. can the line of best fit for the data set have a correlation coefficient of 0.25? explain.
choose the correct answer below.
a. yes. the sign of the correlation coefficient indicates the type of correlation data have. because 0.25 is positive, it is possible for data with a strong positive correlation to have it as the correlation coefficient.
b. no. by definition, data that have a strong positive correlation have a strong linear relationship. the correlation coefficient would be closer to 1 than 0.25 is.
c. no. by definition, data that have a strong positive correlation have a strong linear relationship. the correlation coefficient would be closer to 0 than 0.25 is.
d. yes. by definition, data that have a strong positive correlation have a strong linear relationship. a correlation coefficient of 0.25 indicates a fairly strong correlation.
e. no. by definition, data that have a strong positive correlation have a strong linear relationship. the correlation coefficient would be closer to - 1 than 0.25 is.

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient $r$ ranges from - 1 to 1. A value close to 1 indicates a strong positive linear - relationship, a value close to - 1 indicates a strong negative linear - relationship, and a value close to 0 indicates a weak linear relationship.

Step2: Analyze strong positive correlation

For data with a strong positive correlation, the correlation coefficient should be close to 1. A value of $r = 0.25$ indicates a relatively weak positive linear relationship.

Answer:

B. No. By definition, data that have a strong positive correlation have a strong linear relationship. The correlation coefficient would be closer to 1 than 0.25 is.