Weather Project
Sinusoidal Regressions
Name ________________________
Goal: to model real-life data as a sinusoidal function
You have just received an incredible scholarship, which will allow you to attend college
anywhere in the world. You have narrowed your decision to two cities…one in the northern
hemisphere, one in the southern hemisphere. Both colleges are comparable, so you have
decided to make your final decision based on the city’s weather.
1.
Choose two different cities in the world, one in the northern hemisphere and one in the
southern hemisphere. Please choose a city other than Dallas (or any city in the Metroplex).
If you do not know a city in the southern hemisphere, look it up. You must e mail your 2
cities to me. Once a city has been selected, another student cannot select that city.
2.
Go to http://www.worldclimate.com (or other websites) and find 12 months of temperature
information for your two cities. (You may use the average maximum temperature, or the
24-hr average temperature, or other averages, but try to use the same type of measurement
for both cities.) Please use consistent units of measure, too.
a. Once you have decided on your cities and temperature measurements, please write the
latitude and longitude measurements for each location.
b. Please write all information from your table, and specify the type of data used.
3.
Plot the data using a scatter plot. Sketch a picture of your graph. Repeat for the other city.
4.
Using the information about sinusoidal transformations discussed in class, find a function
that models your data. Repeat for the 2nd city.
5.
Enter the data into your calculator. You may use months for your independent variable,
and you may enter 0 – 11. (What is the period?) In L2 type in each month’s average that
you found.
6.
Use the SinReg on your calculator to determine the sinusoidal equation of each city.
****Your project is due: October 17, 2016 by 9 am
Your completed project will be 3 pages and a Display:
• Pages 1 – 2 will include (one page per city):
o the name of the city.
o one interesting fact about the city.
o a map, pinpointing the location of the city.
o the latitude and longitude of the city,
o the table of data.
o the scatter plot.
o your transformed equation.
o your regression equation.
• Page 3 will consist of the answers to these extension questions.
1.
2.
3.
4.
Compare your transformed equation to your regression equation. Why are they different?
a) Evaluate both of your equations (transformed and regression) for June. What are
the average temperatures for each equation?
b) Compare these numbers with the actual data from the website. Were your numbers
“close?” Why or why not?
c) Find the differences between the actual data and both of your equations.
Describe, in words, the differences and similarities of each city’s temperatures and the
hemisphere.
Look at your “transformed” equation for your Northern Hemisphere city.
a) What is the significance (if any) of the vertical shift?
b) What does the amplitude represent in the context of this problem?
Choose one city. Predict the exact day(s) when the temperature will be exactly 50. Show
work and/or describe how you found your answer.
Create a DISPLAY to showcase your data, graph, equations, and prediction.
****Your project is due: October 17, 2016 by 9 am
Of course, make your project neat, eye-catching, and test worthy!
Impress me!
HOW TO SUBMIT YOUR PROJECT:
1. You will E-MAIL your REPORT to me BEFORE 9:00 am on Monday, October 17, 2016.
2. You will submit your DISPLAY on Monday, October 17 BEFORE 9:00 am to Room US110.
(Super Legal Fine Print: A late fee will be assessed beginning at 9:01 am on Monday, October 17, If you
are not at school on this day, you must have a trusty friend or an amazing parent deliver your project for
you. If this is somehow not possible, you must e-mail me photos of ALL COMPONENTS of your
COMPLETED display before 8:59am. I must be able to ascertain project completion in order to award ontime credit. If this report differs from the electronic version, points will be deducted and the electronic
version will be scored.
The only exception to the strict late fee policy is listed in #2. Sorry, no other exceptions.
(This means that a phone call/e-mail from your parent/guardian does not constitute an exemption from late
fees.)
SUBMIT YOUR ENTIRE PROJECT EARLY AND YOU COULD EARN BONUS POINTS!
Submit all project components by 3:45 PM on Friday, October 14 (+3)
Name of the cities, interesting facts, location, latitude and longitude Data and scatterplot Transformed Equation Regression Equation Comparison of Equations Differences and similarities between cities Northern Hemisphere analysis Prediction Display Quality & Content Display Creativity 10
7
Missing 1 part 4 3 2 0
Missing 2+ parts 5
Organized table and plots with appropriate labels 5
Accurate 5
Accurate 5
Essentially correct. 5
Essentially correct. 4 3 2
Invalid labeling or poor naming. 4 3 2
Partially correct 4 3 2
Partially correct 4 3 2
Partially correct. 4 3 2
Partially correct. 0 Missing table or scatterplot 5
Essentially correct. 5
Essentially correct 10
“Knocks your socks off” impressiveness; exceptionally communicative 5
“Wow! I wish I thought of that!” in terms of creativity & innovativeness 4 3 2
Partially correct. 3
Partially correct 8 6
Meets expectations; may contain some minimal invalidities 0 Missing / mostly incorrect. 0 Missing / mostly incorrect. 3 0
Sub‐‐‐par; no real impact to the project; may be lacking sense of meaningfulness 4 3
Meets expectations; creativity is present and adds to display 2 1 0
Quite minimal; creativity may distract from communication of the content 0 Missing / mostly incorrect. 0 Missing / mostly incorrect. 1 0
Missing / mostly incorrect. 0 Missing / mostly incorrect.