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An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane’s top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of 27 of the company’s planes was taken, and the following model was estimated: y = 0 +11+22+33+   Where y = design effort, in millions of worker-hours  1 = plane’s top speed, in miles per hour  2= plane’s weight, in tons  3 = percentage of parts in common with other models    The estimated regression coefficients were as follows:    b1 = 0.661 b2 = 0.065 b3 = - 0.018    The total sum of squares and regression sum of squares were found to be as follows:    SST = 3.881 and SSR = 3.549    Compute and interpret the coefficient of determination.  Compute the error sum of squares.  Compute the adjusted coefficient of determination. Compute and interpret the coefficient of multiple correlation.

An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane’s top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of 27 of the company’s planes was taken, and the following model was estimated: y = 0 +11+22+33+   Where y = design effort, in millions of worker-hours  1 = plane’s top speed, in miles per hour  2= plane’s weight, in tons  3 = percentage of parts in common with other models    The estimated regression coefficients were as follows:    b1 = 0.661 b2 = 0.065 b3 = - 0.018    The total sum of squares and regression sum of squares were found to be as follows:    SST = 3.881 and SSR = 3.549    Compute and interpret the coefficient of determination.  Compute the error sum of squares.  Compute the adjusted coefficient of determination. Compute and interpret the coefficient of multiple correlation.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane’s top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of 27 of the company’s planes was taken, and the following model was estimated:

y = 0 +11+22+33+

 

Where y = design effort, in millions of worker-hours 

1 = plane’s top speed, in miles per hour 

2= plane’s weight, in tons 

3 = percentage of parts in common with other models 

 

The estimated regression coefficients were as follows: 

 

b1 = 0.661 b2 = 0.065 b3 = - 0.018 

 

The total sum of squares and regression sum of squares were found to be as follows: 

 

SST = 3.881 and SSR = 3.549 

 

  1. Compute and interpret the coefficient of determination. 
  2. Compute the error sum of squares. 
  3. Compute the adjusted coefficient of determination.
  4. Compute and interpret the coefficient of multiple correlation.
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Question An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane's top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of 27 of the company's planes was taken, and the following model was estimated: y=B₁ + B₁₂x₁₂ + B₂X₂ + B3X3 + € Where y = design effort, in millions of worker-hours X₁ = plane's top speed, in miles per hour x₂ = plane's weight, in tons x₂ = percentage of parts in common with other models The estimated regression coefficients were as follows: b₁ = 0.661 b₂ = 0.065 b3 = -0.018 The total sum of squares and regression sum of squares were found to be as follows: SST = 3.881 and SSR = 3.549 a. Compute and interpret the coefficient of determination. b. Compute the error sum of squares. c. Compute the adjusted coefficient of determination. d. Compute and interpret the coefficient of multiple correlation. 1
Transcribed Image Text:Question An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane's top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of 27 of the company's planes was taken, and the following model was estimated: y=B₁ + B₁₂x₁₂ + B₂X₂ + B3X3 + € Where y = design effort, in millions of worker-hours X₁ = plane's top speed, in miles per hour x₂ = plane's weight, in tons x₂ = percentage of parts in common with other models The estimated regression coefficients were as follows: b₁ = 0.661 b₂ = 0.065 b3 = -0.018 The total sum of squares and regression sum of squares were found to be as follows: SST = 3.881 and SSR = 3.549 a. Compute and interpret the coefficient of determination. b. Compute the error sum of squares. c. Compute the adjusted coefficient of determination. d. Compute and interpret the coefficient of multiple correlation. 1
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Compute and interpret the coefficient of multiple correlation.

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