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6. Consider the problem of estimating a production function that expresses the relationship between the level of output of a commodity and the level of input of a factor of production. Assume that you have the production data given in the following table: Table 1: A Sample of Observations on poultry Feed input and Meat output Output y 0.58 1.10 1.20 Input x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1.30 1.95 2.55 2.60 2.90 3.45 3.50 3.60 4.10 4.35 4.40 4.50 (a) Assume that the data can be described by the simple linear regression model y = B₁ + B₂x + e and that all the assumptions hold. Use the least squares principle estimate b₁ and b₂. You may use a calculator for this question. (b) Give an economic interpretation to each of the estimated parameters. (c) Use the results of part (a) to plot the estimated production function.

6. Consider the problem of estimating a production function that expresses the relationship between the level of output of a commodity and the level of input of a factor of production. Assume that you have the production data given in the following table: Table 1: A Sample of Observations on poultry Feed input and Meat output Output y 0.58 1.10 1.20 Input x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1.30 1.95 2.55 2.60 2.90 3.45 3.50 3.60 4.10 4.35 4.40 4.50 (a) Assume that the data can be described by the simple linear regression model y = B₁ + B₂x + e and that all the assumptions hold. Use the least squares principle estimate b₁ and b₂. You may use a calculator for this question. (b) Give an economic interpretation to each of the estimated parameters. (c) Use the results of part (a) to plot the estimated production function.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Please show the work of how to answer part a), b), and c).
6. Consider the problem of estimating a production function that expresses the relationship between the level of output of a commodity and the level of input of a factor of production. Assume that you have the production data given in the following table: Table 1: A Sample of Observations on poultry Feed input and Meat output Output y 0.58 1.10 1.20 Input x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1.30 1.95 2.55 2.60 2.90 3.45 3.50 3.60 4.10 4.35 4.40 4.50 (a) Assume that the data can be described by the simple linear regression model y = B₁ + B₂x + e and that all the assumptions hold. Use the least squares principle estimate b₁ and b2. You may use a calculator for this question. (b) Give an economic interpretation to each of the estimated parameters. (c) Use the results of part (a) to plot the estimated production function.
Transcribed Image Text:6. Consider the problem of estimating a production function that expresses the relationship between the level of output of a commodity and the level of input of a factor of production. Assume that you have the production data given in the following table: Table 1: A Sample of Observations on poultry Feed input and Meat output Output y 0.58 1.10 1.20 Input x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1.30 1.95 2.55 2.60 2.90 3.45 3.50 3.60 4.10 4.35 4.40 4.50 (a) Assume that the data can be described by the simple linear regression model y = B₁ + B₂x + e and that all the assumptions hold. Use the least squares principle estimate b₁ and b2. You may use a calculator for this question. (b) Give an economic interpretation to each of the estimated parameters. (c) Use the results of part (a) to plot the estimated production function.
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