To find the estimated slope ($b_1$) of the regression line, we use the formula:

$b_1 = \frac{n \sum{xy} - \sum{x} \sum{y}}{n \sum{x^2} - (\sum{x})^2}$

Where:

• $n$ is the number of data points (5 in this case),
• $\sum{x}$ is the sum of the list prices,
• $\sum{y}$ is the sum of the number of bids,
• $\sum{xy}$ is the sum of the product of each price and number of bids,
• $\sum{x^2}$ is the sum of the squares of the list prices.

Data

• List Price ($x$): 23, 34, 44, 46, 50
• Number of Bids ($y$): 1, 2, 4, 9, 10

Let's break down the necessary sums:

$\sum{x} = 23 + 34 + 44 + 46 + 50 = 197$ $\sum{y} = 1 + 2 + 4 + 9 + 10 = 26$ $\sum{x^2} = 23^2 + 34^2 + 44^2 + 46^2 + 50^2 = 529 + 1156 + 1936 + 2116 + 2500 = 8237$ $\sum{xy} = (23 \times 1) + (34 \times 2) + (44 \times 4) + (46 \times 9) + (50 \times 10) = 23 + 68 + 176 + 414 + 500 = 1181$

Now, plug these values into the formula for $b_1$:

$b_1 = \frac{5(1181) - (197)(26)}{5(8237) - (197)^2}$ $b_1 = \frac{5905 - 5122}{41185 - 38809}$ $b_1 = \frac{783}{2386}$ $b_1 \approx 0.328$

Thus, the estimated slope is 0.328 (rounded to three decimal places).

Would you like help with the next steps or have any questions about the calculation? Here's a tip: when calculating sums, it's often helpful to organize the data into a table for clarity.

Related Questions:

1. How do you calculate the y-intercept ($b_0$) of the regression line?
2. What is the formula for finding the correlation coefficient $r$?
3. How do you assess the significance of the correlation coefficient?
4. What does a slope of 0.328 mean in the context of this data?
5. What is the next step in calculating the regression equation after finding the slope?

Tip: Always double-check your intermediate calculations, especially when dealing with sums of squares and products. It can help avoid small errors.