Problem Set 3: Curvilinear Regression
Table 1 lists the data obtained from the calibration of an atomic emission
spectrometer's response for a range of alkali ion concentrations.
For concentrations less than 5 ppm, a first order linear calibration curve
is appropriate; for concentrations covering up to 10 ppm, a second order
calibration model must be used.
|
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
|
Requirements
-
For the calibration data in the range of 0-5 ppm
-
Input the data into your spreadsheet and do a least squares first order
fit of the data.
-
Plot the calibration data (using markers only) along with the predicted
calibration curve (using a dashed line and no markers).
-
For an unknown analysis that gave a reading of 4.2 counts/msec, determine
the unknown's concentation and the uncertainly in concentration
in ppm units. Show all calculations; graphically illustrate this
on your calibration plot.
-
For the calibration data in the range of 0-10 ppm
-
Calculate the formula for a second order linear fit of the caliberation
data
-
Plot the calibration data (using markers only) along with the predicted
fit (using a dashed line and no markers) from your model
-
For an unknown analysis that gave a reading of 10.6 counts per msec, calculate
the unknown's concentration in ppm units.