Questions: Use a calculator to find the r-value of these data. Round the value to three decimal places. x y ------ 1 20 3 14 5 10 9 6 16 4 A. 0.901 B. 0.811 C. -0.811 D. -0.901

Solution Steps

The covariance between the variables $X$ and $Y$ is calculated as follows:

$$\text{Cov}(X,Y) = -34.3$$

The standard deviation of $X$ is given by:

$$\sigma_X = 5.933$$

The standard deviation of $Y$ is given by:

$$\sigma_Y = 6.419$$

The correlation coefficient $r$ is calculated using the formula:

$$r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y}$$

Substituting the values:

$$r = \frac{-34.3}{5.933 \times 6.419} = -0.901$$

Final Answer