Before we start working on this laab, let's go back to the data you have created yesterday for the distance and elevation of the twons you had come from. In the table you had for the elevation, add two more columns, one for Latitude and another for Longitude of your town. It is best to have these two columns before the Elevation. Generate a plot that has the Latitude and Longitude on its x and y axes and the elevation on its z axis. Thus, generate a 3-D Surface Grapgh with the three columns of data you have.

**Graphing and Curve
Fitting**

To graph data in Excel, enter your data one variable
per column in consecutive columns. Highlight the data you wish to graph and
then choose *Chart...* from the *Insert* menu. This brings up the *Chart Wizard*. There are many graph
formats to choose from; once you choose one, the wizard will walk you through
customizing your graph. Here is an example of bar charts.

A few items to note while working through the chart
wizard:

- Experiment with highlighting data and labels to see what happens
when you choose different types of graphs. Excel will try to make sense of
your data selection in terms of the graph type, but sometimes the graph
will not be what you expected. Take advantage of the “Press and Hold to
View Sample” option in the first step of the chart wizard.
- The chart options step has lots of graph label customization
options; you can set titles, axis names, and what shows in the legend (or
remove the legend). This is
*not*where you list what the axis labels are. To get data labels (like the animals above) you need to highlight them before graphing or add them in step 2 of the chart wizard. To do this: Click on the “series” tab in step 2, and give the range of cells containing the labels in the “category labels” box. - Once you have completed the chart wizard steps, you still have
options for customizing your graphs.
Double click on something and a panel of options will appear.

Most scientific graphs show the relationship between
two quantities. In Excel, such a relationship is graphed using a scatter plot. Use
a blank sheet by clicking on a Sheet at the bottom. Type in the independent (x) and dependent
variables (y) in adjacent columns; Excel will assume that the left column is
intended for the horizontal axis. Graph a scatter plot of these points by
highlighting the data and then clicking on the chart wizard Be sure to choose
scatter plot and not line graph. Line graphs assume that the horizontal axis
should be marked with counting numbers (1, 2, 3, etc.) and that each
highlighted column is a separate set of vertical axis coordinates.

Read
the directions in the wizard to customize your graph. After you have done all
of the steps, you should see a plot of your data.

Often scientists look at scatter plots like the one above
to determine the trend of the data by finding a function that fits the data
well. Excel has Least Squares Regression routines built in for the most common
behaviors: linear, polynomial, exponential, power, logarithmic.

To
fit a curve to the data in the chart above, first graph it as a scatter plot.
Now you are ready to add a fit. Click
once on any part of the chart, and then choose* Add Trendline* from the *Chart*
menu. You will be asked what kind of trend. Also set the options so that the
formula for the fit and the *r-squared*
value are printed on the graph if desired.

The curve will appear on the graph along with the
data.

As
always, you should use caution when interpreting the *r-squared* value. Mathematically this value must increase for
“curvier” functions such as polynomials of higher degree. Choosing between
different functions should be done visually, not relying solely on the *r-squared* value.

**Lab Activity 2:**

(graphing 1) Use linear regression to find a formula relating the amount of the speciman to the output from the gas chromatograph in the dataset.

http://lib.stat.cmu.edu/DASL/Stories/Chromatography.html

(graphing 2) The inverse of Hubble’s constant can be used
as an estimate of the time since the big bang. Use the data to fit a curve to
find Hubble’s constant (note that the relationship has no intercept).

http://lib.stat.cmu.edu/DASL/Stories/Hubble'sConstant.html

(graphing 3) Investigate Gompertz’ law for population
growth.

http://lib.stat.cmu.edu/DASL/Stories/Gompertz'sLaw.html

(graphing 4) Investigate the relationship between mortality
from breast cancer and average annual temperature..

http://lib.stat.cmu.edu/DASL/Stories/Breastcancer.html

note that the last one is always constant because it is not time-dependent.