Just visually examining the scatter plot data locations gives us a good idea of where the trend line should be located. It also gives us a good idea of a large section of variability when X is above approximately 1.5. This variability could be due to many issues, such as inaccurate data sampling, faulty meter readings, or incorrect preprocessing of the data. Regardless of the reason, we can visually determine that we do not want to include this data in any fit curves or statistics generated by the fit curve.

The scatter plot of the raw data gives a general idea of where a fit curve should be located.

Creating a Curve that Fits the Data

To add a fit curve to the plot:

1. Click on the Line/Scatter Plot 1 to select it, if it is not already selected.
2. In the Property Manager, click on the Plot tab.
3. Scroll all the way down and click the <Click here to add/edit fits> text next to the Fits command.
4. In the Fits dialog, click on the Linear, Y = B * X + A text. In the list, select Power, ln(Y) = B * ln(X) + A. Click the Add button.
5. Click OK and the fit curve is added to the graph.
6. You can change any properties of the fit curve in the Property Manager. For ease of visually determining if the fit curve is a good fit, I’ve changed the line color to red and the line width to 0.030 inches.

The red fit curve fits some of the data, but is skewed because of the variability in the data above X = 1.5.

Creating and Editing a Confidence Interval

To create a confidence interval:

The green confidence interval is added to the plot. Note that the confidence interval is very wide and does not include all the data, despite the high confidence percentage.

Limiting the Fit Curve to Specific Data

Initially the fit curve and confidence interval use all of the data. This gives a skewed result to the fit curve and confidence interval because we know that we want to exclude the upper data points. In the lower section of the plot, the fit curve does not fit the data as well as it could because of this skew. To limit the fit curve to only the desired data:

1. Click on the Fit 1: Power curve to select it.
2. In the Property Manager, click on the Plot tab.
3. Open the Data limits section by clicking on the + next toData limits.
4. Uncheck the box next to the Use curve limits command.
5. Change the Maximum value to 1.65. This value was determined by trying various X values between 1.5 and 2.0 and seeing how the fit curve matched the lower section of data.

The confidence interval fits the data slightly better now, after removing the right section of data from the fit curve data input.

Finalizing the Graph

Although this limited fit curve fits the data better, the final result can be made to make an even better representation of the data. To do so will require removing a few extreme outliers from the data:

1. Click the Tools | Options command.
2. On the left side of the dialog, click Plots. On the right side of the dialog, check the boxes next to Display value on click and Highlight worksheet. Click OK. These options allow you to click on a point on the graph and have that value selected in the worksheet.
3. If the Worksheet Manager is not currently visible, selectView | Managers | Worksheet Manager. Viewing the data and worksheet simultaneously helps when removing data points.
4. Click on the Line/Scatter Plot 1 to select it.
5. On the lower left end of the plot, click on the first point that is above the confidence band. Row 5 is highlighted in theWorksheet Manager.
6. Click on the row 5 in the Worksheet Manager, and press the Delete key on the keyboard. Notice that the data point is immediately removed from the plot and the fit curve is updated.
7. Repeat steps 5 and 6 as necessary until the fit curve fits the data appropriately. I’ve deleted only two points (row 5 and 10) that are visually outside the limits in the image to the right.

After modifying the data slightly, the fit curve and confidence interval show a much better fit to the original data points.