Chapter 11, Problem 1CQ

To determine

Find the correlation coefficient for the given data set.

Answer to Problem 1CQ

The correlation coefficient for the given data set is found to be –0.959.

Explanation of Solution

Interpretation:

The ordered paired values of the random variables x and y are given.

Correlation:

The correlation coefficient, r, between ordered pairs of variables, (x, y) having sample means $\overline{x}$ and $\overline{y}$, sample standard deviations $s_x$ and $s_y$ for a sample of size n is given as $r=\frac{1}{n-1}{\displaystyle \sum \left(\frac{x-\overline{x}}{s_x}\right)\left(\frac{y-\overline{y}}{s_y}\right)}$. The correlation coefficient is useful for measuring the strength of the linear relationship between the two variables.

Software procedure:

Step-by-step procedure to obtain the correlation using the MINITAB software:

• Choose Stat > Basic Statistics > Correlation.
• In Variables, enter the columns of x and y.
• Click OK.

Output using the MINITAB software is given below:

From the output, the correlation coefficient for the given data set is found to be –0.959.