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

$b_1 = \frac{n \sum{x_i y_i} - \sum{x_i} \sum{y_i}}{n \sum{x_i^2} - (\sum{x_i})^2}$

Where:

• $x_i$ are the values of the independent variable (price),
• $y_i$ are the values of the dependent variable (number of bids),
• $n$ is the number of data points.

Let's start by organizing the data:

Price ($x$)	Number of Bids ($y$)	$x \cdot y$	$x^2$
29	1	29	841
33	3	99	1089
34	8	272	1156
36	9	324	1296
46	10	460	2116

Now, calculate the necessary sums:

• $\sum{x_i} = 29 + 33 + 34 + 36 + 46 = 178$
• $\sum{y_i} = 1 + 3 + 8 + 9 + 10 = 31$
• $\sum{x_i y_i} = 29 + 99 + 272 + 324 + 460 = 1184$
• $\sum{x_i^2} = 841 + 1089 + 1156 + 1296 + 2116 = 6498$
• $n = 5$

Substitute these values into the slope formula:

$b_1 = \frac{5 \times 1184 - 178 \times 31}{5 \times 6498 - (178)^2}$

Now, let's calculate this step by step:

$b_1 = \frac{5920 - 5528}{32490 - 31684}$

$b_1 = \frac{392}{806}$

$b_1 = 0.486$

Thus, the estimated slope ($b_1$) is 0.486 (rounded to three decimal places).

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Would you like further details or explanations on any steps? Feel free to ask!

Here are some related questions for you:

1. How do you calculate the estimated intercept $b_0$ in the regression line?
2. How would you calculate the correlation coefficient for this data?
3. What is the significance of the slope in this context?
4. How do you interpret the regression line for predicting the number of bids?
5. Why is it important to check if the correlation coefficient is statistically significant?

Tip: Always check the significance of the regression model (using hypothesis tests) before making predictions to ensure reliability.