1. linear regression quality of the fit and automating the analysis in Excel living with the lab © 2011 David Hall and the LWTL faculty team The Living with the Lab label, the Louisiana Tech Logo, and this copyright notice should not be removed when any part of this work is used by others. This work may not be used for commercial purposes. Inquiries should be addressed to dhall@latech.edu. This presentation on linear regression is based partially on class notes created by Dr. Mark Barker at Louisiana Tech University. good, better and best aren’t very quantitative words to describe the “quality of the fit” good fit better fit best fit

2. living with the lab 2 The content of this presentation is for informational purposes only and is intended only for students attending Louisiana Tech University. The author of this information does not make any claims as to the validity or accuracy of the information or methods presented. The procedures demonstrated here are potentially dangerous and could result in injury or damage. Louisiana Tech University and the State of Louisiana, their officers, employees, agents or volunteers, are not liable or responsible for any injuries, illness, damage or losses which may result from your using the materials or ideas, or from your performing the experiments or procedures depicted in this presentation. If you do not agree, then do not view this content. DISCLAIMER

3. Class Problem Determine the best fit line of “recovery for recycling” versus “year” for 1960, 1970, 1980, 1990, 2000 and 2009. a.Use Excel to set up a table to manually determine the slope m and the y-intercept b. b.Plot the six raw data points versus the fit. Use markers only (with no lines) for the raw data and lines only (no markers) for the fit. 3 living with the lab www.epa.gov Table ES-3. Generation, materials recovery, composting, combustion with energy recovery, and discards of municipal solid waste, 1960-2009, in pounds per person per day http://www.wastexchange.org/upload_publications/MSWintheU.S.2010.pdf

4. living with the lab solution 4 the “coefficient of determination,” more commonly referred to as r 2, will be used to determine the “goodness of the fit”

5. living with the lab 5 coefficient of determination best fit line

6. living with the lab 6 alternate equation for r 2

7. living with the lab 7 solution: adding r 2 to the earlier spreadsheet if r 2 is 0, then there is no apparent relationship between x and y if r 2 is 1, then o x perfectly determines y o the variation in y is wholly due to x o y depends on x and there are no other variables that affect y

8. living with the lab 8 repeat using built-in Excel tools 1.enter x and y data 2.create a scatter plot 3.right click on the markers and select “Add Trendline” 4.select “Linear”, “Display Equation of chart” and “Display R-squared value on chart” STEPS: NOTE: when studying for the next exam, be sure you can solve problems like the one today by hand and using Excel