Reference no: EM13974027
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
|
|
Compute the gain or loss
: Compute the gain or loss recognized by Corporation P if the amount realized on the sale is (1) $175,000, (2) $120,000, or (3) $95,000.
|
|
Did it change your point of view, how, why
: Choose the subject(s). 1500 word thought/analytical essay on one or more of the subjects we've covered. No more than 1500 words.
|
|
Has disney diversified too far in recent years
: Walt Disney: Please evaluate Disney's corporate strategy. Has Disney diversified too far in recent years? Why or why not?
|
|
How did the puritans promote virtue
: What was the Puritan attitude toward marriage and the role of sex in marriage?
|
|
Plot the given points to obtain a scatterplot
: 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.
|
|
Advantages and disadvantages of portfolio analysis
: Describe the advantages and disadvantages of Portfolio Analysis, as it pertains to the BCG Growth-Share Matrix. Explain how Corporate Parenting can contribute to an effective corporate strategy. Discuss how it can relate to a SWOT analysis
|
|
Calculating the return on assets
: The Purple Martin has annual sales of $887,400, total debt of $210,000, total equity of $465,000, and a net profit margin of 5%. What is its return on assets?
|
|
Describe the generic product development process
: Describe the generic product development process described in the chapter. How does the process change for "technology-push" products
|
|
What aspects of this decision would be most difficult
: If your decision came down to two highly qualified candidates, one whose strengths lie primarily in the first six criteria, and the other whose strengths lie primarily in the last five criteria, who would you choose and why? What aspects of this d..
|