To solve this problem, we need to follow these steps:

Step 1: Find the regression coefficients $b_0$ (intercept) and $b_1$ (slope).

We will use the following formulas to calculate these coefficients:

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

2. Intercept $b_0$: $b_0 = \frac{\sum{y_i} - b_1 \sum{x_i}}{n}$

Where:

• $x_i$ = List price
• $y_i$ = Number of bids
• $n$ = Number of data points (which is 5 in this case)

Step 2: Let's calculate the necessary sums from the given data:

Price $x_i$	Bids $y_i$	$x_i y_i$	$x_i^2$
20	3	60	400
39	5	195	1521
43	8	344	1849
44	9	396	1936
47	10	470	2209

Now, let's calculate the necessary sums:

• $\sum x_i = 20 + 39 + 43 + 44 + 47 = 193$
• $\sum y_i = 3 + 5 + 8 + 9 + 10 = 35$
• $\sum (x_i y_i) = 60 + 195 + 344 + 396 + 470 = 1465$
• $\sum (x_i^2) = 400 + 1521 + 1849 + 1936 + 2209 = 7915$

Step 3: Apply the formulas to calculate $b_1$ and $b_0$.

1. Calculate $b_1$: $b_1 = \frac{5 \times 1465 - 193 \times 35}{5 \times 7915 - (193)^2}$ $b_1 = \frac{7325 - 6755}{39575 - 37249}$ $b_1 = \frac{570}{2326}$ $b_1 \approx 0.245$

2. Calculate $b_0$: $b_0 = \frac{35 - 0.245 \times 193}{5}$ $b_0 = \frac{35 - 47.335}{5}$ $b_0 = \frac{-12.335}{5}$ $b_0 \approx -2.467$

Step 4: The estimated regression equation is:

$\hat{y} = -2.467 + 0.245x$

Step 5: Interpretation of the coefficients:

• Slope ($b_1$): The slope is 0.245, meaning that for every 1 unit increase in the price (x), the number of bids (y) increases by approximately 0.245.
• Intercept ($b_0$): The intercept is -2.467, which is the estimated number of bids when the price is 0 (though this is not practically relevant in this case, since prices cannot be 0).

Step 6: If the price increases by 1 unit (say, 1 dollar), the change in the number of bids $\hat{y}$ would be a 0.245 increase in the number of bids.

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Would you like more details about the regression analysis, or do you have any questions? Here are some related questions:

1. What would the estimated number of bids be for a price of $50?
2. How do you interpret the intercept value in this regression model?
3. How can we assess the strength of this regression model using the correlation coefficient?
4. How would this regression equation change if we added more data points?
5. What other factors might influence the number of bids in online auctions?

Tip: Always check the significance of your regression coefficients (especially $b_1$) before making predictions.