Curve-fitting Project – Linear Model (due at the end of Week 5)
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, health, the economy, or something you find interesting. If is strongly recommended that you take advantage of the data search tools provided. Appropriate technology must be used for plots/graphs and determination of the equation of the line and the correlation.
A complete Linear Model Example and Technology Tips are provided in separate documents. Information on some data search tools is also provided.
Tasks for Linear Regression Model (LR)
(LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. An acceptable data set must exhibit a relatively linear pattern. Label appropriately. Each student must use different data.
REQUIRED: Participation in the Linear Model Project Discussion, counting toward your participation grade. In the discussion, your post must include (A) a brief title, (B) informative description of your topic, with x and y variables defined, (C) table of data and a reference for its source, and (D) a rough sketch of the scatterplot, and a of your posting, by the end of Week 4, February 4. (In the completed project, the topic, data set, source should also be included, and the scatterplot must be generated by technology.)
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, or are unsure whether a particular data set is suitable, and your posting provides an opportunity for some feedback. Projects with inappropriate data sets for linear models receive poor grades.
Remark: Students may choose similar topics, but must examine 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.
(LR-2) Using technology, 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.)
(LR-3) Using technology, find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line.
(LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two.
(LR-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?
(LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.
(LR-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.
You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.
Here are Project Suggestions and Data Searches which include PDF guides to helpful search tools.