Precalculus B |Unit 9 Project: Regression Analysis

Introduction:

Pollen is necessary for plants to produce fruit, nuts, and seeds, both for our enjoyment and to enable the plants to reproduce. In the process of pollination, a yellowish powder is transported from plant to plant by wind, insects, or even people, either accidentally or purposely. Yet many people are sensitive to pollen. In fact, during the springtime when airborne pollens are at their highest levels, some people suffer. The level of discomfort depends on the geographic location and type of pollen in the environment. Pollen sensitivity causes inflammation and irritation in the nasal passage, itchy eyes, fatigue, and other symptoms.

The Asthma and Allergy Foundation of America and its research partner, IMS Health, produce a website, pollen.com, which monitors pollen levels in many locations throughout the year.

This dataset was taken from the pollen.com website:

Day	Date	Pollen Level
1	3/3/2016	10.7
2	3/4/2016	9.3
3	3/5/2016	8.9
4	3/6/2016	8.4
5	3/7/2016	7.6
6	3/8/2016	6.7
7	3/9/2016	2.3
8	3/10/2016	3.1
9	3/11/2016	4
10	3/12/2016	8.2
11	3/13/2016	10.9
12	3/14/2016	10.9
13	3/15/2016	10.6
14	3/16/2016	10
15	3/17/2016	9.3
16	3/18/2016	7.6
17	3/19/2016	10.8
18	3/20/2016	10
19	3/21/2016	8.4
20	3/22/2016	9.1
21	3/23/2016	9.7

Overview:You will usedesmos.com to plot the data and create the regression.

Instructions:

1. Plot the Pollen Level data on desmos.com.
2. During which time periods did the pollen level decrease? Increase? (5 points)
3. On which days was the pollen level highest? Lowest? What were those extreme levels? (5 points)
4. Create a regression model for your points you plotted on desmos.com by completing the following process. (5 points)
5. Your points should be in table on desmos.com.
6. Add a regression equation in the form y1 ~ ax1^2 + bx1 + c. (Note: the ~ symbol can be found toward the top left your keyboard in the number row, just to the left of the number one).
7. This creates a quadratic function that best fits the data.
8. Change the scale of the axes until both the data and graph are visible.
9. Export the data and graph to an image file and add it to your report. You should be able to see your data and graph, the equation, and the statistics, residuals, and parameters on the image. If you need directions for exporting an image, they can be foundhere.

(Paste graph here)

1. Create a 2nd regression model using the same process using a cubic function, y1 ~ ax1^3 + bx1^2 + cx^1 + d. Export an image of your graph and add it to your report. (5 points)

(Paste graph here)

1. Compare (analyze) the two regression models, and then answer the following questions. (10 points)
2. Consider intervals where each increase or decrease, and the extreme values. Do these correspond with the data?

1. Which model best fits the data?

1. Why would a straight line not fit the data?