Beer's law scatter plot and trend line (linear regression)

Eng. Haneen Nabil AL-Sbaihi

Environmental Engineering Department

Islamic University of Gaza

In mathematical equations you will encounter in this course, there will be a dependent

variable and an independent variable. Identifying the dependent and independent

variables in a mathematical equation will help you identify what you are solving for in

the equation. The independent variable is a variable whose value determines the value of

the dependent variables. Independent variable is plotted on the Xaxis, and the dependent

variable is plotted on the Y-axis. Other variables may also be present in equations.

These may be constants or other variables. They may be given to you or you may be

required to obtain them by performing curve fitting. The example below illustrates this

point.

Equation 1:

y = mx + C

y = dependent variable

x = independent variable

m and C = constants

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. 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.

The linear equation on chart represents the relationship between Concentration (x) and

Absorbance (y) for the compound.

1. Open Excel program window

2.chane the direction of page by choosing “ left to right” option

3. Add Data Set in Excel

4. To graph the data set click on insert and Plot the graph as XY (Scatter) with data

points only.

5. format the axis’s by right click on the x- axis and choosing axis format option

6. remove the tick that on values in opposite Order option

7. To add a linear regression line on your scatter plot, right click on the data points, and

then click add "trend line". 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.

The equation for the function will be displayed on the chart as shown below.

9. Then format the graph