To find the estimated slope $b_1$ of the regression line, we will 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),
• $x$ represents the list prices of the items,
• $y$ represents the number of bids,
• $\sum{xy}$ is the sum of the products of each pair of $x$ and $y$,
• $\sum{x}$ is the sum of the list prices,
• $\sum{y}$ is the sum of the number of bids,
• $\sum{x^2}$ is the sum of the squares of the list prices.

Step 1: Calculate necessary sums

1. List prices (x): 23, 26, 28, 34, 49
2. Number of bids (y): 1, 2, 5, 9, 10

Let's calculate the sums of the required terms.

• $\sum{x} = 23 + 26 + 28 + 34 + 49 = 160$
• $\sum{y} = 1 + 2 + 5 + 9 + 10 = 27$
• $\sum{x^2} = 23^2 + 26^2 + 28^2 + 34^2 + 49^2 = 529 + 676 + 784 + 1156 + 2401 = 5546$
• $\sum{xy} = (23 \times 1) + (26 \times 2) + (28 \times 5) + (34 \times 9) + (49 \times 10) = 23 + 52 + 140 + 306 + 490 = 1011$

Now, we can substitute these values into the formula for $b_1$:

$b_1 = \frac{5(1011) - (160)(27)}{5(5546) - (160)^2}$ $b_1 = \frac{5055 - 4320}{27730 - 25600}$ $b_1 = \frac{735}{2130}$ $b_1 \approx 0.345$

Conclusion:

The estimated slope $b_1$ of the regression line is approximately 0.345 (rounded to three decimal places).

Would you like to proceed with the next steps or have any questions about this part? Here are some related questions:

1. How do you interpret the meaning of the slope in this context?
2. How would you calculate the estimated intercept $b_0$ of the regression line?
3. What is the formula for the regression line once you have the slope and intercept?
4. How would you use the regression line to predict the number of bids for a given price?
5. How do you calculate the correlation coefficient from the data?

Tip: Ensure you understand how to interpret both the slope and the intercept in real-world scenarios, as they give insight into the relationship between the variables.