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The table contains data and   data for corn. Find a linear regression model for the data where x is supply​ (in billions of​ bushels) and y is price​ (in dollars). Do the same for the data. Find the equilibrium price for corn.
price supply
2.13 6.46

Respuesta :

MrRoyal

A linear regression model is used to show the relationship between variables on a scatter plot

The equilibrium price of corn is $7.71

How to determine the linear regression model?

For the price-demand data for corn, we have the following calculation summary (from a graphing calculator)

  • Sum of X = 14.1
  • Sum of Y = 45.78
  • Mean X = 2.35
  • Mean Y = 7.63
  • Sum of squares (SSX) = 0.1196
  • Sum of products (SP) = 0.5037

So, the regression equation is:

[tex]\^y = 4.21\^x - 2.27[/tex]

For the price-supply data for corn, we have the following calculation summary (from a graphing calculator)

  • Sum of X = 13.62
  • Sum of Y = 50.36
  • Mean X = 2.27
  • Mean Y = 8.3933
  • Sum of squares (SSX) = 0.1206
  • Sum of products (SP) = -0.845

So, the regression equation is:

[tex]\^y = -7.01\^x + 24.30[/tex]

To calculate the equilibrium price, we equate both functions

[tex]4.21\^x - 2.27 = -7.01\^x + 24.30[/tex]

Collect like terms

[tex]7.01\^x + 4.21\^x = 2.27 + 24.30[/tex]

[tex]11.22\^x = 26.57[/tex]

Divide both sides by 11.22

[tex]\^x = 2.37[/tex]

Substitute 2.37 for x in [tex]\^y = 4.21\^x - 2.27[/tex]

[tex]\^y = 4.21 * 2.37 - 2.27[/tex]

[tex]\^y = 7.71[/tex]

Hence, the equilibrium price of corn is $7.71

Read more about linear regression models at:

https://brainly.com/question/17844286

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