Fall 2017 Course
Arithmetic of Fractions Assignment
Getting Started with My Math Lab
PROJECT I - Linear Modeling
The project requires collecting a table of data where the x-value represents time, and the y-value represents some magnitude that is changing roughly linearly. You would then first find a linear model by choosing two appropriate points, and then again an alternate model by using linear regression with the Desmos graphing calculator. Subsequently you would compare the two results in your final write-up.
STEP 1: Find a real-life table of values x, and y, such that their relationship is roughly linearly. This means that as x-values get large, the y values also get large in s steady fashion. Once your graph these points you would notice whether the pattern is roughly linear or not. Here are some options to choose from:
Time and Crime Rate in a particular City
Here x represents time (usually after a given year), and y represents another magnitude. I recommend using City-data.com to find this data easily. For example, for the city of Burbank, CA, you could look at the crime statistics, and choose a table that looks roughly linear.
Crime rates in Burbank by Year |
Type |
2002 |
2003 |
2004 |
2005 |
2006 |
2007 |
2008 |
2009 |
2010 |
2011 |
2012 |
2013 |
2014 |
Murders |
1 |
3 |
4 |
3 |
1 |
3 |
2 |
1 |
0 |
1 |
2 |
0 |
1 |
per 100,000 |
1.0 |
2.9 |
3.8 |
2.9 |
1.0 |
2.9 |
1.9 |
1.0 |
0.0 |
1.0 |
1.9 |
0.0 |
1.0 |
Rapes |
10 |
15 |
14 |
13 |
10 |
14 |
17 |
22 |
13 |
17 |
24 |
13 |
14 |
per 100,000 |
9.6 |
14.4 |
13.4 |
12.4 |
9.5 |
13.3 |
16.4 |
21.3 |
12.6 |
16.3 |
22.8 |
12.4 |
13.3 |
Robberies |
100 |
69 |
82 |
67 |
75 |
98 |
86 |
93 |
98 |
68 |
111 |
51 |
55 |
per 100,000 |
96.2 |
66.4 |
78.4 |
63.9 |
71.4 |
93.4 |
83.0 |
90.1 |
94.9 |
65.0 |
105.7 |
48.7 |
52.4 |
Assaults |
162 |
196 |
162 |
163 |
166 |
159 |
130 |
137 |
110 |
105 |
106 |
107 |
80 |
per 100,000 |
155.8 |
188.5 |
154.9 |
155.5 |
158.0 |
151.6 |
125.4 |
132.7 |
106.5 |
100.4 |
100.9 |
102.2 |
76.2 |
Burglaries |
501 |
500 |
510 |
586 |
567 |
487 |
589 |
499 |
478 |
395 |
383 |
285 |
296 |
per 100,000 |
481.7 |
480.8 |
487.8 |
559.1 |
539.8 |
464.4 |
568.3 |
483.3 |
462.7 |
377.8 |
364.6 |
272.1 |
281.8 |
Thefts |
1,851 |
1,728 |
1,870 |
1,690 |
1,683 |
1,840 |
1,834 |
1,829 |
1,933 |
1,926 |
1,911 |
1,926 |
1,948 |
per 100,000 |
1,779.8 |
1,661.7 |
1,788.6 |
1,612.5 |
1,602.2 |
1,754.5 |
1,769.6 |
1,771.5 |
1,871.2 |
1,842.1 |
1,819.0 |
1,839.1 |
1,854.5 |
Auto thefts |
591 |
466 |
465 |
495 |
471 |
440 |
518 |
335 |
276 |
234 |
199 |
219 |
182 |
per 100,000 |
568.3 |
448.1 |
444.8 |
472.3 |
448.4 |
419.6 |
499.8 |
324.5 |
267.2 |
223.8 |
189.4 |
209.1 |
173.3 |
Arson |
24 |
19 |
10 |
5 |
14 |
18 |
26 |
18 |
8 |
11 |
10 |
6 |
12 |
per 100,000 |
23.1 |
18.3 |
9.6 |
4.8 |
13.3 |
17.2 |
25.1 |
17.4 |
7.7 |
10.5 |
9.5 |
5.7 |
11.4 |
City-data.com crime index (higher means more crime, U.S. average = 287.5) |
211.3 |
202.5 |
205.7 |
199.2 |
192.4 |
202.7 |
208.9 |
195.2 |
181.0 |
165.7 |
180.0 |
148.2 |
145.3 |
An alternative, and even more interesting route is to choose a table where the x-values do not represent time.
Races in Burbank, CA (2013)
- 57,73255.0%White alone
- 28,08426.7%Hispanic
- 12,07211.5%Asian alone
- 3,7663.6%Two or more races
- 1,9371.8%Black alone
- 9290.9%Other race alone
- 850.08%American Indian alone
- 680.06%Native Hawaiian and Other
Pacific Islander alone
You could, for example, collect a table of values where the first column would represent the percentage of White people living in a particular city, and the average API score of the schools in that area. You would do this for several cities, but I recommend collecting at least ten cities.
STEP 2: Use desmos.com to plot a scatter-plot of the points you have collected. Be sure to adjust the window so that the scatter-plot is visible. Print out a copy of the scatter-plot to include it as a diagram in your project.
STEP 3: Now pick two points and the point-slope formula to find the equation of the line that passes through these given two points. Graph this line along with the scatter-plot in desmos, and print a copy of this picture as well.
STEP 4: Find the regression line for the plot by typing y1~mx1+b. Graph this line, and record its slope.
STEP 5: In the write-up of your project discuss the following questions:
- What are the slopes of the two lines you have graphed, and what is their meaning?
- What is the difference between the two models you've found, and which is more representative of the plot of points?
- Are there any outlier points (points which are far away from the models)? Which points are these? What do they represent?