Question

(b) by hand, compute the correlation coefficient. the correlation coefficient is r = 0.902. (round to three decimal places as needed.) (c) determine whether there is a linear relation between x and y. because the correlation coefficient is positive and the absolute value of the correlation coefficient, 0.977, is greater than the critical value for this data set, linear relation exists between x and y. (round to three decimal places as needed.)

Explanation:

Step1: Analyze the correlation coefficient

The correlation coefficient \(r = 0.902\). The sign of \(r\) is positive.

Step2: Check the absolute value

The absolute value \(|r|=0.902\). Since \(|r|\) is close to \(1\) (in general, if \(|r|\gt0.7\) there is a strong linear relationship), and the problem states that the absolute value of the correlation coefficient (which is \(0.977\) in the given context, but we focus on the calculated \(r = 0.902\) for the linear - relationship check) is greater than the critical value (implied by the problem's structure).

Answer:

Since the correlation coefficient \(r = 0.902\) is positive and \(|r| = 0.902\) (and considering the problem's context about the absolute - value condition for linear relationship existence), there is a linear relationship between \(x\) and \(y\).