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Wind Energy Consumption The below table shows the wind energy con- sumption in quadrillions of BTUs in the United States from 2009 through 2013. Year Consumption Xi Yi Linear Model Square Error 2009 0.72 2010 0.92 2011 1.17 2012 1.34 2013 1.60

Wind Energy Consumption The below table shows the wind energy con- sumption in quadrillions of BTUs in the United States from 2009 through 2013. Year Consumption Xi Yi Linear Model Square Error 2009 0.72 2010 0.92 2011 1.17 2012 1.34 2013 1.60

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Wind Energy Consumption** The table below shows the wind energy consumption in quadrillions of BTUs in the United States from 2009 through 2013. | Year | Consumption | \( x_i \) | \( y_i \) | Linear Model | Square Error | |------|-------------|-----------|-----------|--------------|--------------| | 2009 | 0.72 | | | | | | 2010 | 0.92 | | | | | | 2011 | 1.17 | | | | | | 2012 | 1.34 | | | | | | 2013 | 1.60 | | | | | This data provides insights into the growth of wind energy usage over the years, highlighting a steady increase in consumption. The table is intended for educational purposes and can be used to analyze trends, calculate growth rates, or develop linear models to predict future consumption.
Transcribed Image Text:**Wind Energy Consumption** The table below shows the wind energy consumption in quadrillions of BTUs in the United States from 2009 through 2013. | Year | Consumption | \( x_i \) | \( y_i \) | Linear Model | Square Error | |------|-------------|-----------|-----------|--------------|--------------| | 2009 | 0.72 | | | | | | 2010 | 0.92 | | | | | | 2011 | 1.17 | | | | | | 2012 | 1.34 | | | | | | 2013 | 1.60 | | | | | This data provides insights into the growth of wind energy usage over the years, highlighting a steady increase in consumption. The table is intended for educational purposes and can be used to analyze trends, calculate growth rates, or develop linear models to predict future consumption.
3. Find the equation of the least squares regression line for the data as the linear model \( f(x) = a_0 + a_1 x \) in the manner discussed in the textbook using the formula \( A = (X^T X)^{-1}X^T Y \). What are your values for \( a_0 \) and \( a_1 \)?
Transcribed Image Text:3. Find the equation of the least squares regression line for the data as the linear model \( f(x) = a_0 + a_1 x \) in the manner discussed in the textbook using the formula \( A = (X^T X)^{-1}X^T Y \). What are your values for \( a_0 \) and \( a_1 \)?
Expert Solution
Step 1: Determine the arbitrage.

 Let x represent the number of year since 2000. That is x=0 for the year 2000, x=1 for the year 2001 and so on.

Let the linear model be 

f(x)=a0+a1x

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