Problem
Set 2: Sum of Squares and Curvilinear Regression (Individual work required)
I.
Sum of Squares Worksheet Using Cadmium Calibration Data
Using the
data from the cadmiun calibration testing, complete this
spreadsheet as follows:
- Set up a LINEST block and clearly label what
each calculated value represents
- Use the LINEST data to complete the column for
predicted absorbances
- Calculate the residuals
- For each concentration tested, calculate the
mean of the replicates for that concentration
- Calculate the residuals for each data point from
its mean replicate at that concentration
- Calculate the mean of the Absorbance data
- Set up Mean-Centered Absorbance and
Mean-Centered Predicted Absorbance columns
- Calculate each of the following putting the
formula in the designated block:
- Number of Data Points
- Number of Regression Parameters
- Number of Concentrations Used
- Number of Replicate Degress of Freedom (DOF
- Overall Mean Absorbance
- Total Sum of Squares (SS)
- Regression SS
- Coefficient of Determination (Regr SS / Tot SS)
- Residual SS
- Root Mean Square of Residual Error
- Average Percent Error (Use RMS Residual Error
and Overall Absorbance Mean)
- Replicate SS
- Lack of Fit SS
- Mean SS for Lack of Fit
- Mean SS for Replicates
- F Ratio of MSS LOF/MSS Repl
- F Prob.
II.
Curvilinear Regression Problem: The table below lists data obtained
from the calibration of an atomic emission spectrometer's response for a range
of alkali ion concentrations. These 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
|
- 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.
- 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.
- 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