91Ó°ÊÓ

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.

${\mathrm{R}}^2=\frac{{\left[{\displaystyle \underset{}{∑}}\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)\right]}^2}{\underset{}{∑}{\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2}$

Where R means the square of the correlation coefficient.

Standard additions to one solution:

The graph can be drawn using the equation

plot $\underset{\mathrm{Function}\mathrm{to}\mathrm{plot}\mathrm{on}\mathrm{y}-\mathrm{axis}}{\underset{ÁåŸ}{{\mathrm{I}}_{\mathrm{s}+\mathrm{x}}\left(\frac{\mathrm{V}}{{\mathrm{V}}_0}\right)}}$versus $\mathrm{IX}+\frac{{\mathrm{I}}_{\mathrm{x}}}{{\left[\mathrm{X}\right]}_{\mathrm{i}}}\underset{\mathrm{function}\mathrm{to}\mathrm{plot}\mathrm{on}\mathrm{X}-\mathrm{axis}}{\underset{ÁåŸ}{{\left[\mathrm{S}\right]}_{\mathrm{i}}\left(\frac{{\mathrm{V}}_{\mathrm{S}}}{{\mathrm{V}}_0}\right)}}$

Confidence Intervals:

The confidence interval is given by the equation:

Confidence interval $\overline{\mathrm{x}}Â\pm \frac{\mathrm{ts}}{\sqrt{\mathrm{n}}}$

$=\overline{\mathrm{x}}Â\pm {\mathrm{tu}}_{\mathrm{x}}$( since standard uncertaintylocalid="1663560297056" $\left({\mathrm{u}}_{\mathrm{x}}\right)=s/\sqrt{n}$)

Where,

$\overline{\mathrm{x}}$ is mean

s is standard deviation

t is Student's

n is number of measurements

${\mathrm{u}}_{\mathrm{x}}$is standard uncertainty

a)

A spreadsheet with x-axis and y-axis are

Every solution is made to constant volume.

Then [X] / [S] vs ${\mathrm{A}}_{\mathrm{x}}/{\mathrm{A}}_{\mathrm{s}}$ is plotted.

The intercept of the graph is 0.0084 and ${\mathrm{u}}_{\mathrm{m}}=0.0517$, ${\mathrm{u}}_{\mathrm{b}}=0.0335$; the theoretical value of the intercept is 0.

The observed value is less than one standard uncertainty away from 0, which lies with the experimental error of 0.

b)

A spreadsheet with x-axis and y-axis is

The x -intercept is calculated in B19 and B20 and its uncertainty $\left[{\mathrm{C}}_{10}{\mathrm{H}}_8\right]/\left[{\mathrm{C}}_{10}{\mathrm{D}}_8\right]$is 0.598.

The standard uncertainty is$u_x=0.0355$

c)

A spreadsheet with x-axis and y-axis is

The -intercept is calculated in B19 and B 20 and its uncertainty $\left[{\mathrm{C}}_{10}{\mathrm{H}}_8\right]/\left[{\mathrm{C}}_{10}{\mathrm{D}}_8\right]$is 0.598.

The standard uncertainty is $u_x=0.0355$

The students t for 95% confidence and 1 Degree freedom is 12.706. The 95% confidence for $\left[{\mathrm{C}}_{10}{\mathrm{H}}_8\right]/\left[{\mathrm{C}}_{10}{\mathrm{D}}_8\right]$is

$$\begin{gathered} =\overline{\mathrm{x}}Â\pm {\mathrm{tu}}_{\mathrm{x}} \\ =0.598Â\pm \left(12.706\right)\left(0.035\right) \\ =0.598Â\pm 0.451 \end{gathered}$$

The relative uncertainty $=\frac{0.451}{0.598}=75\%$

The uncertainty from a 3-point calibration is large that is 75% because students t is 12.706, where there is only 1 degree of freedom.

If we had just one more data point which gives 2 degree of freedom, the 95% confidence interval would decrease by a factor of 3.