Linear Plot

The Linear Least Squares applet allows you to quickly fit a least-squares line to a set of data. Output includes 95% confidence intervals for the slope and intercept estimates. Also try your hand at a manual fit. Does your best fit by eye match with the least-squares fit?

 

Enter x and y data in the text area. Data will be plotted as they are entered along with a linear least-squares fit. The straight line can be adjusted manually by positioning the cursor toward either end of the line, and clicking and dragging, will allow that end to move. Clicking toward the middle moves the whole line up or down. The least-squares fit minimizes the residual standard deviation based on the sum of the squares of the deviations between the fit and the data.

Exercise. The following concentration vs. absorbance data were collected for a dye. Plot a Beer's Law plot of these data and estimate the extinction coefficient, given that the path length of the sample was 1.17 cm. (You can copy the data from the table and paste it into the applet data area.)

     
Concentration(M) Absorbance  
 
0.000000 0.000  
0.000020 0.150  
0.000040 0.239  
0.000060 0.350  
0.000080 0.480  
0.000100 0.580  

A solution of dye with an unknown concentration was found to have an absorbance of 0.325. What is the concentration of dye in the solution? (You can use the slope and intercept to calculate a value, or you can click on the graph and move the mouse to where the best-fit line has an absorbance value of 0.325. Be careful not to move the fit line!)