Temperature
Background
In
this project you will look at how temperature varies from month to month in
several locations, and model the changes.
1.
What
kind of model do you expect to use?
Why?
Data
The
following table gives the average monthly temperatures in West Palm Beach
(measured at PBI). The averages were
taken using data from 557 months between 1948 and 1994 (data is from www.worldclimate.com).
|
Month |
Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
Oct |
Nov |
Dec |
|
°F |
65.8 |
67.1 |
70.2 |
73.8 |
77.9 |
80.8 |
82.6 |
82.8 |
81.5 |
77.7 |
72.1 |
67.6 |
Go
to www.worldclimate.com
and get similar tables for two other
cities (in different climates). (After
you select your location, select a table of
"Average Temperature".)
Questions
1.
Plot
the values for each of your three cities.
Describe the graphs. What
functions would you use to model these data?
2.
What
are the period, amplitude, vertical shift, and phase shift for each of the
three sets of data? (Estimate the
values as well as you can from the data.)
3.
Using
this information, model each set of data by a trigonometric function. Graph the function with the data. How good is the fit (visually)? Adjust your function to make it fit the data
as well as you can (again, visually).
4.
Use
R2 to describe how good a
fit your final model is for each data set.