Submit Assignment Test1 - Chapters 1 - 5 MAYLINE TORRES Question 7 of 15 Step 1 of 6 01:06:23 The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data. consider the equation of the regression line, $\hat{y}=b_{0}+b_{1} x$, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. \begin{tabular}{|c|c|c|c|c|c|} \hline Price in Dollars & 21 & 23 & 29 & 43 & 50 \\ \hline Number of Bids & 1 & 2 & 4 & 5 & 7 \\ \hline \end{tabular} Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Answer How to enter your answer (opens in new window) 0.5 Points Keyboard Shortcuts
Solution
Step 1 ：Given the prices and bids data as follows: prices = [21, 23, 29, 43, 50] and bids = [1, 2, 4, 5, 7].
Step 2 ：Calculate the sum of the prices (sum_x) and the sum of the bids (sum_y). We get sum_x = 166 and sum_y = 19.
Step 3 ：Calculate the sum of the squares of the prices (sum_x2) and the sum of the squares of the bids (sum_y2). We get sum_x2 = 6160 and sum_y2 = 95.
Step 4 ：Calculate the sum of the products of paired data (sum_xy). We get sum_xy = 748.
Step 5 ：Calculate the correlation coefficient (r) using the formula: \(r = \frac{n \cdot \Sigma xy - \Sigma x \cdot \Sigma y}{\sqrt{(n \cdot \Sigma x^2 - (\Sigma x)^2) \cdot (n \cdot \Sigma y^2 - (\Sigma y)^2)}}\). We get r = 0.9636176976435222.
Step 6 ：Calculate the mean of the prices (mean_x) and the mean of the bids (mean_y). We get mean_x = 33.2 and mean_y = 3.8.
Step 7 ：Calculate the standard deviation of the prices (Sx) and the standard deviation of the bids (Sy) using the formula: \(S = \sqrt{\frac{1}{n-1} \cdot \Sigma (x - \text{mean}(x))^2}\). We get Sx = 12.735776379946374 and Sy = 2.3874672772626644.
Step 8 ：Calculate the estimated slope (b1) using the formula: \(b1 = r \cdot \frac{Sy}{Sx}\). We get b1 = 0.18064118372379778.
Step 9 ：Round the estimated slope to three decimal places. The final answer is \(\boxed{0.181}\).
