Curve-fitting Project - Linear Model (due at the end of Week 5) Instructions For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r2 (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below. A Linear Model Example and Technology Tips are provided in separate documents. Tasks for Linear Regression Model (LR)
1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label appropriately. (Highly recommended: Post this information in the Linear Model Project discussion as well as in your completed project. Include a brief informative description in the title of your posting. Each student must use different data.) The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the project, and your posting provides an opportunity for some feedback. Remark: Students may choose similar topics, but must have different data sets. For example, several students may be interested in a particular Olympic sport, and that is fine, but they must collect different data, perhaps from different events or different gender.
2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.)
3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line.
4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two.
5) Find and state the value of r2, the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?
6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.
7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting.
This project explores the relationship between the year of a summer Olympic Games and the gold medal time recorded for the Men's marathon distance running event. In particular, this project will evaluate the linearity of the relationship between the two variables. The data was obtained from the website www.olympic.org, and consists of pairs of data, where each pair includes the year of the event and the recorded time in hours, minutes, seconds, and decimal fractions of seconds. In order to plot these points, all of the times in the data set will be converted to minutes.
The data is shown in the table below:
|
Year
|
Time
|
Time (minutes)
|
|
2012
|
2:08:01
|
128.02
|
|
2008
|
2:06:32
|
126.53
|
|
2004
|
2:10:55
|
130.92
|
|
2000
|
2:10:11
|
130.18
|
|
1996
|
2:12:36
|
132.60
|
|
1992
|
2:13:23
|
133.38
|
|
1988
|
2:10:32
|
130.53
|
|
1984
|
2:09:21
|
129.35
|
|
1980
|
2:11:03.0
|
131.05
|
|
1976
|
2:09:55.0
|
129.92
|
|
1972
|
2:12:19.8
|
132.33
|
|
1968
|
2:20:26.4
|
140.44
|
|
1964
|
2:12:11.2
|
132.19
|
|
1960
|
2:15:16.2
|
135.27
|
|
1956
|
2:25:00
|
145.00
|
|
1952
|
2:23:03.2
|
143.05
|
|
1948
|
2:34:51.6
|
154.86
|
|
1936
|
2:29:19.2
|
149.32
|
|
1932
|
2:31:36
|
151.60
|
|
1928
|
2:32.57
|
152.95
|
|
1924
|
2:41:22.6
|
161.38
|
|
1920
|
2:32:35.8
|
152.60
|
|
1912
|
2:36:54.8
|
156.91
|
|
1908
|
2:55:18.4
|
175.31
|
|
1904
|
3:28:53.0
|
208.88
|
|
1900
|
2:59:45.0
|
179.75
|
|
1896
|
2:58:50
|
178.83
|