Questions: The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks. Completion Percentage 55 55.5 57 57.5 58.5 Interception Percentage 4 3.5 3 2.5 1.5 Calculate the correlation coefficient, r. Round your answer to three decimal places.

The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks. Completion Percentage 55 55.5 57 57.5 58.5 Interception Percentage 4 3.5 3 2.5 1.5 Calculate the correlation coefficient, r. Round your answer to three decimal places.
Transcript text: The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks. \begin{tabular}{|c|c|c|c|c|c|} \hline Completion Percentage & 55 & 55.5 & 57 & 57.5 & 58.5 \\ \hline Interception Percentage & 4 & 3.5 & 3 & 2.5 & 1.5 \\ \hline \end{tabular} Calculate the correlation coefficient, $r$. Round your answer to three decimal places.
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Solution

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Solution Steps

Step 1: Calculate the Mean of Both Sets of Values

The mean of X, \(\bar{X}\), is 56.7. The mean of Y, \(\bar{Y}\), is 2.9.

Step 2: Compute the Deviations from the Mean

The deviations for each value in X and Y are calculated from their respective means.

Step 3: Calculate the Products of These Deviations

Each pair of deviations (from X and Y) is multiplied to calculate the products.

Step 4: Sum Up All the Products

The sum of all the products of deviations is -5.4.

Step 5: Calculate the Squared Deviations from the Mean

The squared deviations for each value in X and Y are calculated.

Step 6: Sum Up the Squared Deviations for Each Set

The sum of squared deviations for X is 8.300, and for Y is 3.7.

Step 7: Calculate the Correlation Coefficient

The correlation coefficient, \(r\), is calculated using the formula and is -0.974.

Final Answer:

The correlation coefficient, rounded to 3 decimal places, is -0.974.

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