Chapter 5, Problem 5.EE

a)

Interpretation Introduction

Interpretation:

The least squares slope and intercept and their standard deviations and the theoretical value has to be calculated.

Concept Introduction:

LINEST:

The LINEST is a Microsoft excel function which is uses the least squares method to measure the statistics for a straight line and array describing that line it is built-in function that can be categorized.

LINEARITY:

It is measure of how well a calibration curve follows a straight line and displaying that the response is proportional to the quantity of the analyte.

${\text{R}}^{\text{2}}\text{=}\frac{{\left[{\displaystyle \sum \left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)\right]}^{\text{2}}}{{\displaystyle \sum {\left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}^{\text{2}}}{\displaystyle \sum {\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)}^{\text{2}}}}$

Where R means square of correlation coefficient.

Standard additions to one solution:

The graph can be drawn using the equation

$\text{plot}\underset{\text{Function}\text{to}\text{plot}\text{on}\text{y-axis}}{\underbrace{{\text{I}}_{\text{S+X}}\left(\frac{\text{V}}{{\text{V}}_{\text{0}}}\right)}}\text{versus }{\text{I}}_{\text{X}}\text{+}\frac{{\text{I}}_{\text{X}}}{{\left[\text{X}\right]}_{\text{i}}}\underset{\text{function}\text{to}\text{plot}\text{on}\text{x-axis}}{\underbrace{{\left[\text{S}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{S}}}{{\text{V}}_{\text{0}}}\right)}}$

Where X-intercept is ${\left[\text{X}\right]}_{\text{i}}$

b)

Interpretation Introduction

Interpretation:

The standard uncertainty ${\text{u}}_{\text{x}}$ for the peak ratio has to be calculated.

Concept Introduction:

LINEST:

The LINEST is a Microsoft excel function which is uses the least squares method to measure the statistics for a straight line and array describing that line it is built-in function that can be categorized.

LINEARITY:

It is measure of how well a calibration curve follows a straight line and displaying that the response is proportional to the quantity of the analyte.

${\text{R}}^{\text{2}}\text{=}\frac{{\left[{\displaystyle \sum \left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)\right]}^{\text{2}}}{{\displaystyle \sum {\left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}^{\text{2}}}{\displaystyle \sum {\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)}^{\text{2}}}}$

Where R means square of correlation coefficient.

Standard additions to one solution:

The graph can be drawn using the equation

$\text{plot}\underset{\text{Function}\text{to}\text{plot}\text{on}\text{y-axis}}{\underbrace{{\text{I}}_{\text{S+X}}\left(\frac{\text{V}}{{\text{V}}_{\text{0}}}\right)}}\text{versus }{\text{I}}_{\text{X}}\text{+}\frac{{\text{I}}_{\text{X}}}{{\left[\text{X}\right]}_{\text{i}}}\underset{\text{function}\text{to}\text{plot}\text{on}\text{x-axis}}{\underbrace{{\left[\text{S}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{S}}}{{\text{V}}_{\text{0}}}\right)}}$

Where X-intercept is ${\left[\text{X}\right]}_{\text{i}}$

c)

Interpretation Introduction

Interpretation:

The value of $\text{95\%}$ confidence interval and $1$ degree freedom has to be calculated.

Concept Introduction:

LINEST:

The LINEST is a Microsoft excel function which is uses the least squares method to measure the statistics for a straight line and array describing that line it is built-in function that can be categorized.

LINEARITY:

It is measure of how well a calibration curve follows a straight line and displaying that the response is proportional to the quantity of the analyte.

${\text{R}}^{\text{2}}\text{=}\frac{{\left[{\displaystyle \sum \left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)\right]}^{\text{2}}}{{\displaystyle \sum {\left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}^{\text{2}}}{\displaystyle \sum {\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)}^{\text{2}}}}$

Where R means square of correlation coefficient.

Confidence Intervals:

The confidence interval is given by the equation:

$\begin{array}{l}\text{Confidence interval = }\overline{x}\pm \frac{ts}{\sqrt{n}}\\ =\overline{x}\pm t{u}_x(\text{since standard uncertainty(}{u}_x)=s/\sqrt{n}\text{) }\end{array}$

Where,

$\overline{x}$ is mean

$s$ is standard deviation

$t$ is Student’s t

n is number of measurements

$u_x$ is standard uncertainty