Marine Pollution

Part 1. Background Information

The following table shows paired values of TBT and TI.  Edit the command for defining musselData, and enter this data set.

Results of TBT and Thickness Index analyses 
in the tissue samples of mussels 
            μg/g TBT     Thickness Index    
                 .04                  .40     
                 .11                  .42
                 .50                  .43
                 .60                  .43
                 .73                  .46
                 .77                  .46 
               1.75                  .48
               4.31                  .53
               1.66                  .50
               3.56                  .56
                 .27                  .48
                 .45                  .45
                 .74                  .44
               1.75                  .48
                 .04                  .42
                 .04                  .39

musselData  :=  { {.04,  .40},  ?? ? }

Part 2. Plotting the Data

Edit and use the ListPlot command below to generate a scatter plot of the data.  (If you don't remember how, review the Functions Defined by Data module -- or, type ?ListPlot for a summary of the command).

ListPlot[?? ?]

Use plot "options" to enhance your graphs.  The general format for plot options is 
            ListPlot[data, option1, option2, option3, ...]
Some general examples and specific recommendations for the musselData plot:

You can specify the y range:
            PlotRange->{ymin, ymax}
You can set point size to give all points a diameter d:
            Prolog->AbsolutePointSize[d]
You can set teh color of plotted points with specified red, green and blue components each between 0 and 1:
            PlotStyle->RGBColor[r, g, b]
You can label your axes:
            AxesLabel->{"xlabel", "ylabel"}

Complete and enter your enhanced plot command below.

ListPlot[musselData,  ?? ?]

What sort of relationship seems to exist between the concentration of TBT in the cells of the mussels and the thickness of their shells? 
Type response here:

Part 3. Fitting a Line to the Data

Enter the following command for plotting a generic line:

\(a\  = \ 1; 
b\  = \ 0; 
Plot[a*x + b, \ {x, \ \(-1\), \ 5}]\)

The next Mathematica commands allows us to plot the mussel data and line y=ax+b together, with any desired values of a and b.  First we construct the plot of the line and name it linePlot.  Then we plot the data and name the result musselPlot.  The final command you should read as "Plot, in one graph, the scatter plot of our data and the graph of the function ax+b as x ranges from -1 to 5."  Activate these commands, and resize the plot as necessary.

\(a\  = \ 1; \ \ \ b\  = \ 0; 

    linePlot\  = \ 
      Plot[a*x + b, \ {x, \ \(-1\), \ 5}, \ PlotStyle -> RGBColor[0, 0, 1], \ 
        DisplayFunction -> Identity]; 

    musselPlot\  = \ 
      ListPlot[musselData, Prolog -> AbsolutePointSize[6], \ 
        PlotStyle -> RGBColor[1, 0, 0], \ 
        AxesLabel -> {"ug/g TBT", "Thickness Index"}, \ 
        DisplayFunction -> Identity\ ]; 

    Show[linePlot, \ musselPlot, \ DisplayFunction -> $DisplayFunction]\)

Mathematica Note:
Graphics can be displayed or hidden by using the DisplayFunction option.  DisplayFunction->Identity will display nothing.  Reset the DisplayFunction by using DisplayFunction->$DisplayFunction.

Mathematica has a built-in routine, Fit, for fitting a line to a data set.  Use the function by entering the next line to calculate the best-fitting line.

fitLine  =  Fit[musselData,  {1,  x},  x]

Next, we include the graph of this least squares line with the other two graphs. Type the above equation into the fitPlot command below (or use cut and paste), and activate it.

fitPlot  =  Plot[?? ?, {x, -1.2, 4.5} ]

Now activate the following command to see all three graphs together, and see how close you came with your "eyeball" estimate.

Show[musselPlot,  linePlot,  fitPlot,  
      DisplayFunction -> $DisplayFunction]

Part 4. Summary