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)
2.196.35
2.237.39
2.347.64
2.437.77
2.428.23
2.397.74
2.598.24
2.426.82

Step 2: Linear regression formula

The general formula for the linear regression line is: y=mx+by = mx + b Where:

  • mm is the slope
  • bb is the y-intercept

To find the slope (mm) and intercept (bb), we need to apply the following formulas:

m=n(xy)(x)(y)n(x2)(x)2m = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{n(\sum{x^2}) - (\sum{x})^2} b=ym(x)nb = \frac{\sum{y} - m(\sum{x})}{n}

Where nn is the number of data points.

Step 3: Compute values

Let's compute the necessary sums:

  1. x\sum{x} (sum of supply values)
  2. y\sum{y} (sum of price values)
  3. xy\sum{xy} (sum of products of price and supply)
  4. x2\sum{x^2} (sum of squared supply values)

I will now calculate the values.The linear regression model for the price-supply data is:

y=0.1334x+1.3727y = 0.1334x + 1.3727

Where:

  • xx is the supply in billions of bushels
  • yy 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?

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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