I. Cadmium Calibration Problem

Cadmium is a toxic heavy metal found to be present above the EPA drinking water limit of 5 parts-per-billion in approximately half of the contaminated sites on the National Priority List.  Cadmium is extracted from the mining process for zinc or copper; cadmium is used extensively in batteries, pigments, and plastics.

A leading university is developing a mobile technology to measure Cd levels in surface water; portable instrumentation would provide real-time analysis and prevent having to transport samples back to a fixed laboratory for analysis. Recent testing with a bench scale model was conducted over a range of cadmium concentrations between 250 parts-per-trillion and the 5 parts-per-billion EPA limit.  Approximately 10-25 challenges at each concentration were made separately to fully characterize the initial performance of this mobile technology.

The datasheet from these experiments provide Cd concentrations, source intensities (I_o), and intensities (I) present after passing through the sample.

Requirements:  Create an excel spreadsheet and do the following:

1. Add columns showing the transmittance and absorbance for each measurement 

2. Use the absorbance-concentration data to conduct a linear regression; use the regression results to add a column showing predicted absorbances for each concentration

3.  Generate a plot clearly showing the calibration points and the regression line using the format described in class.  Also clearly shown the calibration equation for these data.

4.  A water sample collected near a suspected Cd-contaminated site solution was analyzed ten times and yielded an average absorbance of 0.253 AU.  Calculate the amount of Cd predicted by the regression for this reading; clearly show all equations and work.

II. Curvilinear Regression Problem:  Table 1 lists the data obtained from the calibration of an atomic emission spectrometer's response for a range of alkali ion concentrations.  The data are nonlinear above 5.0 ppm.

Concentration (ppm)	Counts/msec
0.2	0.8
0.5	1.3
1.0	2.2
2.0	3.7
3.0	5.1
4.0	6.5
5.0	7.8
6.0	8.9
7.0	9.9
8.0	10.5
9.0	10.8
10.0	11.0

1. Using all points, conduct a 2nd order fit of these data; plot the predicted curve, the data points, and write the equation for the predicted curve that includes appropriate units.

2. For an unknown analysis that gave a reading of 10.6 counts/msec, determine the unknown's concentration.  Show all calculations on a separate sheet of paper; graphically illustrate this on your calibration plot.

3. Using all points, conduct a 1st order fit of the data, show the equation, and compare the Coefficients of Determination for the 1st and 2nd order fits.  State what percent of the overall variability is accounted for in each of these fits