Questions: Question 5 of 9, Step 3 of 3 7 / 17 Correct Incorrect Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction. Price in Dollars 20 29 32 35 41 Number of Bids 11 12 13 15 18 Copy Data Step 3 of 3 : Calculate the correlation coefficient, r. Round your answer to three decimal places.

Question 5 of 9, Step 3 of 3 7 / 17 Correct Incorrect Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction. Price in Dollars 20 29 32 35 41 Number of Bids 11 12 13 15 18 Copy Data Step 3 of 3 : Calculate the correlation coefficient, r. Round your answer to three decimal places.
Transcript text: Question 5 of 9, Step 3 of 3 $7 / 17$ 1 Correct Incorrect Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction. \begin{tabular}{|c|l|l|l|l|l|} \hline Price in Dollars & 20 & 29 & 32 & 35 & 41 \\ \hline Number of Bids & 11 & 12 & 13 & 15 & 18 \\ \hline \end{tabular} Copy Data Step 3 of 3 : Calculate the correlation coefficient, $r$. Round your answer to three decimal places. Answer Tables Keypad How to enter your answer (opens in new window) Keyboard Shortcuts
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Solution

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Solution Steps

Step 1: Calculate the means of x and y values

The mean of x values ($\bar{x}$) is 13.8, and the mean of y values ($\bar{y}$) is 31.4.

Step 2: Compute the sum of the product of differences from the mean for each pair of x and y

The sum of the product of differences is 80.4.

Step 3: Calculate the sum of squares of differences from the mean for all x and y values

The sum of squares for x values is 30.800, and for y values is 241.200.

Step 4: Calculate the correlation coefficient

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} = 0.933$$

Final Answer:

The correlation coefficient, rounded to 3 decimal places, is 0.933.

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