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To make the calculations simpler, before computing the regression line, subtract 2000 from each of the years so that for example, the year 2009 is given as 9 and the first (x,y) data point is therefore (9, 0.72) and likewise for the other years. Fill in the x, and y, data in the third and fourth columns of the table. As discussed in Section 2.6 of the textbook, use the set of (x,y) data points to assemble the matrices X and Y. See Example 7 page 101 in the textbook, or any of the assigned homework problems in Section 2.6 for an example of this. Find the the equation of the least squares regression line for the data as the linear model f(x) = ao + a₁x in the manner discussed in the textbook using the formula A = (XTX)-¹XTY. What are your values for ao and a₁? 1 Use the linear model to create a table of estimated values for wind energy consumption. Add this information to the above table in the fifth column. For each year compare the estimated values with the data by computing the square of the error. Add this information to the above table in the last column. Characterize the overall accuracy of the linear model by computing the sum of the square errors. Use the linear model to predict the wind energy consumption for 2014 and 2015.

To make the calculations simpler, before computing the regression line, subtract 2000 from each of the years so that for example, the year 2009 is given as 9 and the first (x,y) data point is therefore (9, 0.72) and likewise for the other years. Fill in the x, and y, data in the third and fourth columns of the table. As discussed in Section 2.6 of the textbook, use the set of (x,y) data points to assemble the matrices X and Y. See Example 7 page 101 in the textbook, or any of the assigned homework problems in Section 2.6 for an example of this. Find the the equation of the least squares regression line for the data as the linear model f(x) = ao + a₁x in the manner discussed in the textbook using the formula A = (XTX)-¹XTY. What are your values for ao and a₁? 1 Use the linear model to create a table of estimated values for wind energy consumption. Add this information to the above table in the fifth column. For each year compare the estimated values with the data by computing the square of the error. Add this information to the above table in the last column. Characterize the overall accuracy of the linear model by computing the sum of the square errors. Use the linear model to predict the wind energy consumption for 2014 and 2015.

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
Problem 1P
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To make the calculations simpler, before computing the regression line, subtract 2000 from each of the years so that for example, the year 2009 is given as 9 and the first (x,y) data point is therefore (9, 0.72) and likewise for the other years. Fill in the x, and y, data in the third and fourth columns of the table. As discussed in Section 2.6 of the textbook, use the set of (x,y) data points to assemble the matrices X and Y. See Example 7 page 101 in the textbook, or any of the assigned homework problems in Section 2.6 for an example of this. Find the the equation of the least squares regression line for the data as the linear model f(x) = ao + a₁x in the manner discussed in the textbook using the formula A = (XTX)-¹XTY. What are your values for ao and a₁? 1 Use the linear model to create a table of estimated values for wind energy consumption. Add this information to the above table in the fifth column. For each year compare the estimated values with the data by computing the square of the error. Add this information to the above table in the last column. Characterize the overall accuracy of the linear model by computing the sum of the square errors. Use the linear model to predict the wind energy consumption for 2014 and 2015.
Transcribed Image Text:To make the calculations simpler, before computing the regression line, subtract 2000 from each of the years so that for example, the year 2009 is given as 9 and the first (x,y) data point is therefore (9, 0.72) and likewise for the other years. Fill in the x, and y, data in the third and fourth columns of the table. As discussed in Section 2.6 of the textbook, use the set of (x,y) data points to assemble the matrices X and Y. See Example 7 page 101 in the textbook, or any of the assigned homework problems in Section 2.6 for an example of this. Find the the equation of the least squares regression line for the data as the linear model f(x) = ao + a₁x in the manner discussed in the textbook using the formula A = (XTX)-¹XTY. What are your values for ao and a₁? 1 Use the linear model to create a table of estimated values for wind energy consumption. Add this information to the above table in the fifth column. For each year compare the estimated values with the data by computing the square of the error. Add this information to the above table in the last column. Characterize the overall accuracy of the linear model by computing the sum of the square errors. Use the linear model to predict the wind energy consumption for 2014 and 2015.
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 2009 0.72 2010 0.92 2011 1.17 2012 1.34 2013 1.60 Linear Model Square Error
Transcribed Image Text: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 2009 0.72 2010 0.92 2011 1.17 2012 1.34 2013 1.60 Linear Model Square Error
Expert Solution
Step 1: Write the given information.
YearConsuptionxiyiLinear ModelSquared Error
20090.7290.72

20100.92100.92

20111.17111.17

20121.34121.34

20131.6131.6

The linear model for the data set is given as f(x)=a0+a1⋅x.

A equals left parenthesis X to the power of T X right parenthesis to the power of negative 1 end exponent X to the power of T Y A equals open square brackets table row cell a subscript 0 end cell row cell a subscript 1 end cell end table close square brackets

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