Question

for the following data set, (a) draw a scatter diagram, (b) compute the correlation coefficient, and (c) comment on the type of relation that appears to exist between x and y
(a) which of the following scatter diagrams corresponds to the given data?
(b) compute the correlation coefficient
(c) what type of relation appears to exist be
the linear correlation coefficient is close to so linear relation exists between x and y

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 \(1\). If \(r = 1\), there is a perfect positive linear relationship. If \(r=-1\), there is a perfect negative linear relationship. If \(r = 0\), there is no linear relationship.

Step2: Analyze the given \(r\) value

We are given \(r\approx0.972\). Since \(0.972\) is close to \(1\).

Answer:

The linear correlation coefficient is close to \(1\) so a strong positive linear relation exists between \(x\) and \(y\).