Question

on ten randomly selected winter weekdays this year, lisa records the daily high outdoor temperature and the amount of time she takes to drive to work, as shown in the table below.
time taken to drive to work vs. daily high outdoor temperature
use the drop - down menus to choose the correct answer for each blank.
the linear correlation coefficient of this data is approximately choose...
therefore, there is a choose... correlation between the daily high outdoor temperature and the amount of time lisa takes to drive to work in the winter.

Explanation:

Step1: Input data into calculator

Input the \(x\) - values (temperatures: \(10,14,20,22,28,32,38,40,44,45\)) and \(y\) - values (times: \(60,63,53,57,52,52,42,38,31,32\)) into a graphing calculator or statistical software.

Step2: Calculate correlation coefficient

Using the formula for the linear correlation coefficient \(r=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}\) or the built - in function of the calculator/software. After calculation, we find that \(r\approx - 0.96\).

Step3: Interpret correlation

Since \(r=-0.96\) and \(|r|\) is close to \(1\) (\(0.96\gt0.7\) which is a common threshold for a strong correlation), and \(r\lt0\).

Answer:

The linear correlation coefficient of this data is approximately \(-0.96\). Therefore, there is a strong negative correlation between the daily high outdoor temperature and the amount of time Lisa takes to drive to work in the winter.