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, yˆ=b0+b1x
, 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.

Price in Dollars	25
27
35
37
38
Number of Bids	1
2
3
5
8
Table


Step 1 of 6 :  Find the estimated slope. Round your answer to three decimal places.

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 $ = number of data points
- $ x $ = list price
- $ y $ = number of bids
- $ \sum xy $ = sum of the product of each pair of $ (x, y) $
- $ \sum x^2 $ = sum of the squares of each $ x $ value

### Given Data:
\[
\text{Price (x)}: 25, 27, 35, 37, 38
\]
\[
\text{Number of Bids (y)}: 1, 2, 3, 5, 8
\]

### Calculations:
1. Compute the necessary sums:
   - $ \sum x $ = 25 + 27 + 35 + 37 + 38
   - $ \sum y $ = 1 + 2 + 3 + 5 + 8
   - $ \sum xy $ = (25)(1) + (27)(2) + (35)(3) + (37)(5) + (38)(8)
   - $ \sum x^2 $ = 25^2 + 27^2 + 35^2 + 37^2 + 38^2

2. Substitute these sums into the formula for $ b_1 $.

I'll perform these calculations step-by-step.The estimated slope ($ b_1 $) of the regression line is approximately $ 0.401 $ when rounded to three decimal places.

Would you like a breakdown of this calculation or have any other questions?

### Related Questions:
1. How do you calculate the y-intercept ($ b_0 $) of the regression line?
2. What is the equation of the regression line using this slope?
3. How can you test if the correlation coefficient is statistically significant?
4. How do residuals help in analyzing the accuracy of the regression model?
5. What would be the predicted number of bids for an item listed at $40?

### Tip:
In regression analysis, the slope ($ b_1 $) tells you the average change in the response variable (number of bids) for each one-unit increase in the predictor variable (price).

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, ŷ = b0 + b1x, 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.

Price in Dollars: 25, 27, 35, 37, 38
Number of Bids: 1, 2, 3, 5, 8

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Learn how to estimate the slope of a linear regression line based on the relationship between list price and number of bids in online auctions. This problem covers key statistical concepts, including the slope formula and linear regression analysis. Data: Price in dollars (25, 27, 35, 37, 38), Number of bids (1, 2, 3, 5, 8). Suitable for undergraduate students.

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