# 5.4 Sinusoidal Regression Project

In this task, we gather and examine a periodic data set that can be modelled well with a sinusoidal function.

Page 1: A Title page with a short paragraph that summarizes the project.

Page 2: The data set (as a table – google sheet?) along with the source of the data set.

Page 3: A screen shot of the graph (axes labelled); and a screen shot of the regression equation.

Page 4: An informed discussion of the model in the context of the data.

# Ideas for data

1. Compare the amount of daylight hours over a year in two latitudes – eg, in Victoria vs Iqaluit;
2. Plot sunrise times for one year on the same graph as sunset times for one location;
3. Compare average high with average low temperature for one location for a full year;
4. Plot the percent visible of the face of the moon for four months;
5. Find two famous ferris wheels, other than the London Eye, and compare height/duration on the same graph
6. Mark a bike tyre with chalk. Track the height of the chalk above the ground when (a) the bike is in the lowest gear; when (b) the bike is in the highest gear; for one full rotation of the pedals.
7. Compare volume displacement in one cylinder in two different car engines, when running at 2000 rpm.
8. Breathing rhythms: obtain data for volume of air in lungs over time, compare during rest, during exercise.
9. Take tide data for one day during a full moon, and from the same location during a new moon.
10. Other tide data – eg, compare Victoria water height for two days with Bay of Fundy water height for the same two days.
11. Race Rocks current speed data. Compare one day during a full moon and one day during a new moon.
12. The angle of the sun above the horizon at noon every day for a year, in one location.

Here’s a bunch more ideas

# Partner or Individual?

Should you choose to compare two related data sets (such as most of the ideas above), then you may submit one project between two. A comparison leads to interesting discussion. If going solo, its ok to have just one data set.

# Discussion

Address the following in the discussion:

• Technical details of the regression model – domain and range.
• An overall opinion of whether or not the trend of the model is a good fit for the trend of the data, as anticipated by your context.
• An example of an interval or point where the model fits the data quite well – how small does the error get?
• An example of an interval or point where the model does not fit very well – how big does the error get?
• An example of interpolation – use the model to predict an value within the data set.
• An example of extrapolation – use the model to predict a value beyond the data set. Test this value against a real world value if possible.
• One or two observations of your own: (eg, “I notice that…” or “I wonder …”) regarding your data set, your model and your context.

# Assessment

Pages 1 & 2 will be marked out of 20.

Looking for – a sufficient; well managed; well presented & sourced data set;

Pages 3 & 4 will be marked out of 20.

Looking for – correctly and well presented graph & calculated regression equation. A coherent, interesting and informative discussion – good questions asked with reasonable and criticized answers given.

You may submit the project twice, feedback will be given on the first copy.