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	21
23
29
43
50
Number of Bids	1
2
4
5
7


Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.


To find the y-intercept (\(b_0\)) of the regression line \( \hat{y} = b_0 + b_1x \), we need the following steps.

### 1. Calculate the means of both \(x\) (price) and \(y\) (number of bids).
Let’s define the variables:
- \( x \) is the price in dollars.
- \( y \) is the number of bids.

The data is:
- \( x = \{21, 23, 29, 43, 50\} \)
- \( y = \{1, 2, 4, 5, 7\} \)

We need to compute the mean of both \(x\) and \(y\):
\[
\bar{x} = \frac{\sum x_i}{n}, \quad \bar{y} = \frac{\sum y_i}{n}
\]
where \( n = 5 \) (the number of data points).

### 2. Compute the slope (\(b_1\)).
The formula for \(b_1\) (slope) is:
\[
b_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}
\]

### 3. Find the y-intercept (\(b_0\)).
Once we know \(b_1\), the y-intercept is found using:
\[
b_0 = \bar{y} - b_1 \bar{x}
\]

Let’s calculate the necessary values to find the y-intercept.The estimated y-intercept (\(b_0\)) of the regression line is approximately \(-2.197\) (rounded to three decimal places).

Would you like further details or have any questions about this calculation?

Here are five related questions for further exploration:
1. How is the slope (\(b_1\)) of the regression line interpreted in this context?
2. How do we determine if the correlation coefficient is statistically significant?
3. What assumptions must be met to use linear regression?
4. How would the regression line change if one of the data points were an outlier?
5. How can you use the regression line to make predictions?

**Tip:** Always check the correlation coefficient before using a regression model to make predictions. A weak correlation suggests the model may not be reliable.

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: 21, 23, 29, 43, 50. Number of Bids: 1, 2, 4, 5, 7. Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Learn how to calculate the y-intercept of the regression line for predicting the number of bids an item will receive based on its list price. This problem involves key concepts like linear regression, slope, and y-intercept calculation using data points for prices and bids from online auctions. Suitable for Grades 10-12 students.

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