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Transport of Sulfite Ions from Blood Cells

Keywords: nonlinear regression, exponential function, heterscedasticity, autocorrelated residuals


The data related to the transport of sulfite ions from blood cells suspended in a salt solution. The chloride concentration (%) was measured over a period of about 8 minutes as a continuous curve generated from electrical potentials. The data given here were digitized from the curve at 10 second intervals.

The theory of ion transport suggested that the concentration asymptote exponentially, i.e.,

Chloride = q1{1 - q2exp(- q3Time)}

Variable Description

Time Elapsed time in minutes
Chloride Chloride concentration (%)


Data File (tab-delimited text)


Sredni, J. (1970). Problems of Design, Estimation and Lack of Fit in Model Building. PhD Thesis, University of Wisconsin-Madison.

Bates, D. M., and Watts, D. G. (1988). Nonlinear Regression Analysis and Its Applications. Wiley, New York.

The data were originally collected by W. H. Dennis and P. Wood at the University of Wisconsin. The data were obtained electronically from the web site Data sets from "Nonlinear Regression Analysis" maintained by Douglas Bates.


> chloride <- read.table("chloride.txt",header=T)
> attach(chloride)
> plot(Time,Chloride)
> out <- nls(Chloride~cbind(1,exp(-b*Time)),start=list(b=0.1),algorithm="plinear")
> summary(out)

Formula: Chloride ~ cbind(1, exp( - b * Time))

       Value Std. Error  t value
b   0.158523   0.010444  15.1784
   39.094900   0.974427  40.1209
  -32.387600   0.561816 -57.6481

Residual standard error: 0.191962 on 51 degrees of freedom

Correlation of Parameter Estimates:
  0.911 -0.950
> lines(Time,fitted(out),col=2)

chloride1.gif (6412 bytes)

> plot(fitted(out),residuals(out))

chloride2.gif (6140 bytes)



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