Chapter 4, Problem 4.27P

Interpretation Introduction

Interpretation:

The slope, intercept and standard deviation for the straight line drawn through the given point has to be calculated also a graph showing the three point has to be drawn.

Concept Introduction:

Equation of a line:

The equation of straight line is:

$\begin{array}{l}y=mx+b\\ y=[m(\pm u_m)]x+[b(\pm u_b)]\end{array}$

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:

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