Math Problem Statement
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
2.19 6.35 2.01 9.94 2.23 7.39 2.12 9.27 2.34 7.64 2.23 8.28 2.43 7.77 2.38 8.03 2.42 8.23 2.39 7.74 2.59 8.24 2.42 6.82 . . . Question content area right 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).
Solution
Step 1: Organize the data
To find a linear regression model for the price-supply data, we will first organize the data. The table provides two sets of data### Step 1: Organize the data
To find a linear regression model for the price-supply data, we will first organize the data. The table provides two sets of
- Supply (x): in billions of bushels
- Price (y): in dollars per bushel
Here’s the price-supply data that we have:
Price (y) | Supply (x) |
---|---|
2.19 | 6.35 |
2.23 | 7.39 |
2.34 | 7.64 |
2.43 | 7.77 |
2.42 | 8.23 |
2.39 | 7.74 |
2.59 | 8.24 |
2.42 | 6.82 |
Step 2: Linear regression formula
The general formula for the linear regression line is: Where:
- is the slope
- is the y-intercept
To find the slope () and intercept (), we need to apply the following formulas:
Where is the number of data points.
Step 3: Compute values
Let's compute the necessary sums:
- (sum of supply values)
- (sum of price values)
- (sum of products of price and supply)
- (sum of squared supply values)
I will now calculate the values.The linear regression model for the price-supply data is:
Where:
- is the supply in billions of bushels
- is the price in dollars per bushel
Next, we will repeat the same process to find the linear regression model for the price-demand data. Would you like me to proceed with that part as well?
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Regression
Algebra
Statistics
Formulas
Linear regression equation: y = mx + b
Slope formula: m = [n(Σxy) - (Σx)(Σy)] / [n(Σx^2) - (Σx)^2]
Intercept formula: b = [Σy - m(Σx)] / n
Theorems
Least Squares Method
Suitable Grade Level
Grades 10-12
Related Recommendation
Linear Regression Models for Corn Price-Supply and Price-Demand Data
Linear Regression for Corn Price-Supply and Price-Demand Data
Price-Supply and Price-Demand Linear Regression Models for Corn
Quadratic and Linear Regression Models for Price-Demand and Supply
Linear Regression Model for Supply and Demand Equilibrium