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.
failed

Solution

failed
failed

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.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The nurse understands which medication may cause gynecological malignancies females? Oxytocin Raloxifene Thalidomide Diethylstilbestrol
failedAnswered
View society as a structure with interrelated parts designed to meet the biological and social needs of individuals who make up that society. Conflict Theorists Structural Functionalists Social Individualists Symbolic Interactionists
failedAnswered
I'm sorry, but you haven't provided the text containing the question. Could you please provide the text you need analyzed?
failedAnswered
Lab Assessment Question 19, P6-53 (similar to) Part 4 of 4 HW Score: 55%, 11 of 20 points Points: 0 of 1 Save (Comprehensive problem) You would like to have 54,000 in 13 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 6 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 6 percent on this deposit.) c. At the end of five years, you will receive 15,000 and deposit this in the bank toward your goal of 54,000 at the end of year 13. In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? (Again, assume you can earn 6 percent on your deposits.) a. How much must you deposit annually to accumulate this amount? 2859.85 (Round to the nearest cent.) b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should the lump-sum deposit be? 25317.31 (Round to the nearest cent.) c. If you deposit 15,000 received at the end of five years in the bank, what will the amount grow to by the end of year 13? 23907.72 (Round to the nearest cent) In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? (Round to the nearest cent.)
failedAnswered
The Ten Commandments were important to the development of modern democracy because they: A. created the basic political processes used in modern direct democracies. B. established moral principles that apply in many legal systems today. C. defined a set of human rights that no government could take from citizens. D. combined Judeo-Christian and Greco-Roman beliefs for the first time.