To find the linear regression model for the price-supply data, where $x$ is the supply (in billions of bushels) and $y$ is the price (in dollars), we need to follow these steps:

Steps to Solve:

1. Organize the data: You have two sets of data points, one for supply and one for price.

   • Supply data $(x)$: 6.34, 7.36, 7.73, 7.98, 8.08, 8.08, 7.86, 8.32, 6.97
   • Price data $(y)$: 2.11, 2.22, 2.39, 2.47, 2.46, 2.36, 2.54, 2.47

2. Set up the form of the linear regression equation: The linear regression equation is typically of the form: $y = mx + b$ where:

   • $m$ is the slope of the line.
   • $b$ is the y-intercept.

3. Calculate the slope $m$: The formula for the slope is: $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$ where:

   • $n$ is the number of data points.
   • $\sum xy$ is the sum of the product of each $x$ and $y$ value.
   • $\sum x$ and $\sum y$ are the sums of $x$ and $y$ values, respectively.
   • $\sum x^2$ is the sum of the squares of the $x$ values.

4. Calculate the y-intercept $b$: The formula for the y-intercept is: $b = \frac{\sum y - m(\sum x)}{n}$

Let's proceed with calculating the slope and y-intercept for the price-supply data first.

I'll compute it for you now.The linear regression model for the price-supply data is:

$y = 0.174x + 1.048$

where $x$ is the supply (in billions of bushels) and $y$ is the price (in dollars).

Next, let's follow the same process to find the linear regression model for the price-demand data.

Could you please confirm the demand data so we can proceed, or should I assume it's the following set based on typical questions?

• Demand (billion bushels): 9.93, 9.46, 8.45, 8.08, etc.

Let me know if you have any questions or if you'd like more detailed explanations. Here are 5 related questions for deeper understanding:

1. How is the slope $m$ in the regression model interpreted in terms of supply and price?
2. What impact does the y-intercept $b$ have on the linear regression model?
3. How would adding more data points affect the accuracy of the regression model?
4. Can non-linear models be more appropriate than linear models for price-supply relationships?
5. How does the correlation between supply and price affect the regression model?

Tip: A positive slope in a linear regression means the dependent variable (price) increases as the independent variable (supply) increases, and vice versa.