In the manufacture of synthetic fiber, the fiber is often “set” by subjecting it to high temperatures. The object is to improve the shrinkage properties of the fiber. In a test of 23 yarn specimens, the relationship between temperature in °C (x) and shrinkage in % (y) was summarized by the least-squares line y = −12.789 + 0.133x. The total sum of square was ∑ni=1(yi−y⎯⎯)2∑i=1n(yi−y¯)2 = 57.313, and the estimated error variance was s2 = 0.0670. Compute the coefficient of determination r 2. Round the answer to three decimal places

In the manufacture of synthetic fiber, the fiber is often “set” by subjecting it to high temperatures. The object is to improve the shrinkage properties of the fiber. In a test of 23 yarn specimens, the relationship between temperature in °C (x) and shrinkage in % (y) was summarized by the least-squares line y = −12.789 + 0.133x. The total sum of square was ∑ni=1(yi−y⎯⎯)2∑i=1n(yi−y¯)2 = 57.313, and the estimated error variance was s2 = 0.0670. Compute the coefficient of determination r 2. Round the answer to three decimal places

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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