Questions: Scatter Plots and Correlation What type of correlation does the following dataset appear to have? x 0 1 2 3 4 5 y 18 2 24 11 14 3 No Correlation Negative Correlation Positive Correlation

Solution Steps

The covariance \( \text{Cov}(X,Y) \) between the datasets \( X \) and \( Y \) is calculated as: \[ \text{Cov}(X,Y) = -5.2 \] The standard deviation of \( X \) is: \[ \sigma_X = 1.87 \] The standard deviation of \( Y \) is: \[ \sigma_Y = 8.56 \]

The correlation coefficient \( r \) is computed using the formula: \[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \] Substituting the values: \[ r = \frac{-5.2}{1.87 \times 8.56} \approx -0.32 \]

Since the correlation coefficient \( r \) is less than 0, it indicates a negative correlation between the variables \( X \) and \( Y \).

Final Answer