The table contains price dash supply data and price dash demand data for corn. Find a linear regression model for the price dash supply data where x is supply​ (in billions of​ bushels) and y is price​ (in dollars). Do the same for the price dash demand data. Find the equilibrium price for corn.
Price left parenthesis $ divided by bu right parenthesis
Supply left parenthesis billion bu right parenthesis
Price left parenthesis $ divided by bu right parenthesis
Demand left parenthesis billion bu right parenthesis

2.11
6.34
2.07
9.93
2.22
7.36
2.14
9.46
2.39
7.73
2.25
8.45
2.47
7.98
2.37
8.08
2.46
8.08
2.36
7.86
2.54
8.32
2.47
6.97
.
.
.
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Part 1
Find a linear regression model for the price dash supply data where x is supply​ (in billions of​ bushels) and y is price​ (in dollars).

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.

The table contains price-supply data and price-demand data for corn. Find a linear regression model for the price-supply data where x is supply​ (in billions of​ bushels) and y is price​ (in dollars). Do the same for the price-demand data. Find the equilibrium price for corn. Price left parenthesis $ divided by bu right parenthesis Supply left parenthesis billion bu right parenthesis Price left parenthesis $ divided by bu right parenthesis Demand left parenthesis billion bu right parenthesis.

Discover how to find the linear regression model for price-supply and price-demand data for corn. This problem involves calculating the slope and y-intercept using key linear regression formulas. Suitable for college students or advanced high school learners.

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