Questions: Calculate the correlation coefficient for the following ordered pairs. x 3 7 1 7 7 y 6 8 4 4 7 r= (Round to three decimal places as needed.)

Solution Steps

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

$$\text{Cov}(X,Y) = 2.5$$

The standard deviation of $X$ is given by:

$$\sigma_X = 2.828$$

The standard deviation of $Y$ is given by:

$$\sigma_Y = 1.789$$

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

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

Substituting the values we have:

$$r = \frac{2.5}{2.828 \times 1.789} \approx 0.494$$

Final Answer