Chapter 4, Problem 4.26P

Interpretation Introduction

Interpretation:

For the given points of a straight line, the slope and intercept and their uncertainties with reasonable number of significant figures has to be given.

Concept Introduction:

Standard deviation of y: $s_y$

The standard deviation of y is:

${\sigma }_y\approx s_y=\sqrt{\frac{{\displaystyle \sum (d_i{}^2)}}{n-2}}$

Standard uncertainty of slope and intercept:

The standard uncertainty of slope is:

${\text{u}}_m^2=\frac{s_y^{2}n}{D}$

The standard uncertainty of intercept is:

${\text{u}}_b^2=\frac{s_y^2{\displaystyle \sum (x_i{}^2)}}{D}$

To Give: The slope and intercept and their uncertainties with reasonable number of significant figures for a given points of a straight line.