n the accompanying table, x is the tensile force applied to a steel specimen in thousands of pounds, and y is the resulting elongation in thousands of an inch: X 1 2 3 4 5 Y 14 33 40 63 76 85 a) Find the equation of the least squares line, and use it to predict the elongation when the tensile force is 3.5 thousand pounds. b) Construct a 95% confidence interval for B, the elongation per thousand pounds of tensile stress; c) Find 95% limits of prediction for the elongation of a specimen with x 3.5 thousand pounds.

n the accompanying table, x is the tensile force applied to a steel specimen in thousands of pounds, and y is the resulting elongation in thousands of an inch: X 1 2 3 4 5 Y 14 33 40 63 76 85 a) Find the equation of the least squares line, and use it to predict the elongation when the tensile force is 3.5 thousand pounds. b) Construct a 95% confidence interval for B, the elongation per thousand pounds of tensile stress; c) Find 95% limits of prediction for the elongation of a specimen with x 3.5 thousand pounds.

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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Estimation

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Problem #3

In the accompanying table, $ x $ is the tensile force applied to a steel specimen in thousands of pounds, and $ y $ is the resulting elongation in thousands of an inch:

\[
\begin{array}{c|ccccc}
X & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
Y & 14 & 33 & 40 & 63 & 76 & 85 \\
\end{array}
\]

a) Find the equation of the least squares line, and use it to predict the elongation when the tensile force is 3.5 thousand pounds.

b) Construct a 95% confidence interval for $ \beta $, the elongation per thousand pounds of tensile stress.

c) Find 95% limits of prediction for the elongation of a specimen with $ x = 3.5 $ thousand pounds.

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