Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b.151 -2A =b=1-1 -2...a. The orthogonal projection of b onto Col A is b= (Simplify your answer.)b. A least-squares solution of Ax = b is x= (Simplify your answer.)3.

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Answered: Find (a) the orthogonal projection of b…

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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Use the factorization A = QR to find the least-squares solution of Ax = b. 23 A = 2 4 1 1 5 -8 b= 6 2 II 2/3 1/3 - 2/3 2/3 1/3 2/3 - 35 01
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 315.27 28.31 11.24 0.002 Elevation -31.812 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.8% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = + x (b) For each 1000-foot increase in elevation,…
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 316.62 28.31 11.24 0.002 Elevation -30.516 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares…
H1.
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 14 HA A = - 18 b= 1 14 7 4 a. The orthogonal projection of b onto Col A is b = (Simplify your answers.)
3 Find the least squares cubic equation that best fits the points: (-2,-2), (-1, 1), (0, 1), (1, 2), (2, 2).

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Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 1 5 1 -2 A = b= 1 -1 -2 ... a. The orthogonal projection of b onto Col A is b= (Simplify your answer.) b. A least-squares solution of Ax = b is x= (Simplify your answer.) 3.