HW5 - sense i.e that minimizes ∑ n i =1 y i-a-bx i 2 3...

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Math 104 Fall 2009 Homework 4 Due Wednesday, November 4, 2009 1. Very simple linear regression. Consider the three points ± 0 1 ² , ± 1 - 1 ² , ± 2 - 2 ² . What is the equation of the line that best fits those three points, in the sense of least squares? 2. Simple linear regression. You have pairs of real-valued data ( x i ,y i ), i = 1 ,...,n (for instance, x i may be the square footage of a home and y i its sale price). What is the equation of the regression line y = a + bx in terms of the x i ’s and y i ’s? The regression line is the line that best fits the points in a least squares
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Unformatted text preview: sense, i.e. that minimizes ∑ n i =1 ( y i-a-bx i ) 2 . 3. Projections (a) Check that A ( A * A )-1 A * defines an orthogonal projector (assume that A * A is invertible). What does this project onto? (b) Check that A * ( AA * )-1 A also defines an orthogonal projector (assume that AA * is invertible). What does this project onto? 4. Exercise 4.4, Chapter 4 of Trefethen-Bau (justify your answer). 5. Exercise 5.4, Chapter 5 of Trefethen-Bau. 1...
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