Question

find the correlation coefficient of the line of best fit for the points $(-3, -40)$, $(1, 12)$, $(5, 72)$, and $(7, 137)$. explain how you got your answer. use the coefficient to describe the correlation of this data

Explanation:

Step1: Input data into calculator

Using a graphing calculator (e.g., TI - 84 Plus), enter the \(x\) - values (\(-3\), \(1\), \(5\), \(7\)) into list \(L_1\) and the \(y\) - values (\(-40\), \(12\), \(72\), \(137\)) into list \(L_2\).

Step2: Calculate linear regression

Go to the STAT → CALC menu and select LinReg(a + bx) (or LinReg(ax + b) depending on the calculator model). With L_1 as the \(x\) - list and L_2 as the \(y\) - list, and ensure DiagnosticOn (if needed to get the correlation coefficient \(r\)).
When we run the linear regression, we get the correlation coefficient \(r\approx0.99\).

Answer:

The correlation coefficient \(r\approx0.99\). Since \(r\) is very close to \(1\) (where \(r = 1\) represents a perfect positive linear correlation), this data has a very strong positive linear correlation.