Math 107 Curve-fitting Project – Linear Model-Free Solution
Curve-fitting Project – Linear Model
For this assignment you should
– collect data exhibiting a relatively linear trend,
– plot the data and the line,
– find the equation of line of best fit,
– find the slope and interpret the meaning of the slope,
– use the linear equation to make a prediction of y at x that is not in your data set
– find r2 (coefficient of determination) and r (correlation coefficient). Discuss your findings.
Your topic and set of data may be related to sport, health, food, your work, a hobby, or something you find interesting.
Suggested sources of data are given in the attached file Appendix B and in links below.
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.
2) Plot the points (x, y) to obtain a scatter plot. 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 scatter plot.
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, scatter plot, line, r, or estimate, etc.) that you found particularly important or interesting.
Here are some possible topics and sources of data:
Health. You can select all your data from Appendix B.pdf. File has extensive numerical data related to health exams, body temperature, weight, body mass index and many other collected information that you can use in this project.
Food. On website http://www.acaloriecounter.com/fast-food.php you can find information about calories, fat and sodium content in different food depending on serving size. Select at least 8 brands and look up, for example, the fat content and the associated calorie total per serving. Make a quick plot for yourself to “eyeball” whether the data exhibit a relatively linear trend. (If so, proceed. If not, try a different type of food.) After you find the line of best fit, use your line to make a prediction corresponding to a fat amount not occurring in your data set.) Alternative: Look up carbohydrate content and associated calorie total per serving.
Baseball. If you are baseball fan you can use website http://www.baseball-reference.com/ ; to find two variables that may exhibit a linear relationship. For instance, for each team for a particular season in baseball, find the total runs scored and the number of wins.
Olympic sport. Go to http://www.databaseolympics.com/ and collect data for winners in the event for at least 8 Olympic games (dating back to at least 1980). (Example: Winning times in Men’s 400 m dash). Make a quick plot for yourself to “eyeball” whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different event.) After you find the line of best fit, use your line to make a prediction for the next Olympics (2014 for a winter event or 2016 for a summer event)