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Beer's law scatter plot and trendline (linear regression)

       Tutorial programs > MS Excel > Beer's law scatter plot and trendline (linear regression)


A calibration curve or standard curve is usually using series of standard solutions known concentrations is prepared and measured using spectrophometer instrument to determine the unknown concentration of sample. It is represent a graph where concentration is plotted against absorbance then a straight line (Beer's Law) is fit to the data that you obtained and the resulting equation is used to convert absorbance of the unknown sample into concentration. This equation of this line by first finding the slop (m= y2 - y1/x2 - x1) and changing that into
y = mx + c

For this experiment, the slope and intercept of that line provide a relationship between absorbance and concentration that determined by Beer's Law
.

Lambert-Beer Law is used to determine concentration [M, mM, or mM] from Absorbance [No unit], if the molar extinction coefficient e [M-1cm-1] of a compound and the path length of the cuvette [cm] that the distance light passes through the solution are known. The formula of this relationship:
A =
e * l * c    thus, the concentration can be calculated by:  c=A/e l
According the Lambert-Beer law, an increase in the concentration of a solution leads to a increase in the absorbance as linear.
Sources: Wikipedia Molar absorptivity and Wikipedia Lambert Law.

To plot any data in excel, you should enter the data, create a scatter plot with only Markers from data, and then add linear regression (trendline) to make Excel the better line fit to the data and can be used as formula (y=mx+c)to calculate the concentration of unknown compound. You can find the steps for how to plot data using Excel 2007 in "MS Excel/How to draw the graphical relation between two variables section". The linear equation on chart represents the relationship between Concentration (x) and Absorbance (y) for the compound.

To add linear regression line on your scatter plot, right click on the data points, and then click add "trendline". Choose "linear" as the type of Trend/Regression. Select check boxes of "Display Equation on chart" and "Display R-squared value on chart", and then click "OK".
The R-squared value gives the square of the Pearson correlation coefficient of the linear regression. The closer value of R to 1 means relationship between x and y is very exactly and line fit to data.

See the xls file attachment for this tutorial.




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