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