Question

temperature: celsius vs. fahrenheit
based on your dufs description, which of the following correlation coefficients best describes the relationship?
○ r = 0.1
○ r = 1
○ r = -1
○ r = 0.90

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. The value of \(r\) ranges from \(- 1\) to \(1\). A value of \(r = 1\) indicates a perfect positive linear relationship, \(r=-1\) indicates a perfect negative linear relationship, \(r = 0\) indicates no linear relationship. A value close to \(1\) (but not equal to \(1\)) indicates a strong positive linear relationship, and a value close to \(-1\) (but not equal to \(-1\)) indicates a strong negative linear relationship.

Step2: Analyze the scatter - plot

In the given scatter - plot of Celsius vs Fahrenheit, as Fahrenheit temperature increases, Celsius temperature also increases. So, it is a positive relationship. The points are not perfectly on a straight line, so \(r
eq1\). But the points are closely clustered around an imaginary straight line, which means the relationship is strong. A value of \(r = 0.1\) would indicate a very weak positive relationship, which is not the case here. A value of \(r=-1\) would indicate a negative relationship, which is incorrect. A value of \(r = 0.90\) (close to \(1\)) indicates a strong positive linear relationship, which matches the scatter - plot.

Answer:

\(r = 0.90\)