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).