x1,2,5,6 y5,0,4,3,3,3,2,6 Complete parts (a) through (e), given Σx = 14, Σy = 152, Σx2 = 66, Σy2 = 6114, Σxy = 457, and r ≈ −0.9894. Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers to four decimal places.) x = y = yhat = ___+__ x Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 = explained % unexplained % (f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y?

x1,2,5,6 y5,0,4,3,3,3,2,6 Complete parts (a) through (e), given Σx = 14, Σy = 152, Σx2 = 66, Σy2 = 6114, Σxy = 457, and r ≈ −0.9894. Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers to four decimal places.) x = y = yhat = _+ x Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 = explained % unexplained % (f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 34EQ

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Question

x1,2,5,6

y5,0,4,3,3,3,2,6

Complete parts (a) through (e), given Σx = 14, Σy = 152, Σx² = 66, Σy² = 6114, Σxy = 457, and r ≈ −0.9894.

Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers to four decimal places.)

x	=
y	=
yhat	=	___+__ x

Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to four decimal places. Round your answers for the percentages to two decimal place.)