Carbon Dioxide Levels in the Atmosphere

The purpose of this project is to find an equationy=f(x) that fits the yearlyCO2 data that has been recorded in Hawaii since 1959. The hope is that theequation will accurately predict future CO2 levels in the atmosphere for thenext several years. Extrapolating the curve far into the future would onlybe justified if there is a verified theory explaining credibly why the equationwe come up with might be right. For our equation, there is no such theory.This is solely an exercise in exploratory data analysis.Details.OPTION 1: Download the filenoaaco2.txtfrom Can-vas, open it with a plain-text editor and read the data into R using theread.tablecommand.orOPTION 2: enter a subset of the data byhand into two variables. Only do one of the two options!!OPTION 1:To open the file, the recommended software on a windowsmachine like all those at Murphy isNotepad. Whether you use a windowsmachine or a Mac, the main thing is to know how to specify the exact locationof the file. Opening the file withNotepadallows you to save it in whateverdirectory you wish. One thing that works for me is to click on ’save as’ andthen specify the filec:\users\amatchett\noaaco2.txtexcept that I need to leave off the .txt because that is automatically includedbyNotepad. After saving the file in that way, I can read it with the commandjoe <- read.table(“c:/users/amatchett/noaaco2.txt”)Then the two variables you need are “year” and “mean co2 level.” Seewhat R is calling them – probablyV1andV2. You can use these two variablesas is by referring to them asjoe$V1andjoe$V2. However, it is better torename themxandyby the commands,x <- joe$V1andy <- joe$V2which is what I will do.OPTION 2:To enter a subset of the data by hand, first enter a variablexas follows:x <- c(1960,1970,1980,1990,2000,2010,2015).That is 7 x-values. Then enter into a variabley, the seven mean co2 levelsfor the same years as those entered intox. The first two are:1
y <- c(316.91, 325.68and so on, getting the other 5 mean co2 levels from the data file.With either method, as long as your variables arexandy, you are all setto fit a curve. First use the plot command to see what a scatter plot lookslike. The command for that isplot(y~x) .This puts the y-variable onthe vertical axis and the x-variable on the horizontal axes. Then (a) find thecorrelation coefficient ofxwithy.Then improve this correlation coefficient as much as possible using trans-formations in the familiesw←sqrt(y+c) andw←sqrt(y−c)wherecis a constant. You may limit your search to integer values ofc.(b) Give your highest correlation coefficient and give the transformation thatproduces it. (c) Regresswuponx(R function:lm(w~x)), and give theequation of the least squares line withwas the dependent variable andxasthe independent variable. (d) Solve the equation in part (c) foryin termsofx, and give the resulting equation. (e) Make a scatter plot of the original(x,y) data points, and superimpose the graph of the equation from part (d)on the scatter plot (R function:curve(f(x), add=TRUE).(f) If you entered the data by hand using 7 data points, give the atmo-spheric CO2 concentrations that your equation predicts for the years 2019and 2020.(f) If yourxandyvariables contain the full data lists from 1959 to 2020,give the atmospheric co2 concentrations predicted by your equation for theyears 2022 and 2023.Type up your results as an informative and short technical report. Usefull sentences. Your paper should occupy a little less than one side of a page,and it should be completely understandable to people who do not know whatthe assignment was. Include everything from parts (a) to (f) in your paper.You may sketch the scatter plot and superimposed curve by hand, or importit into your paper electronically. However, do not let it take up too muchspace!In typing up your report follow the Technical Report Guidelines postedin Canvas. The project may be done individually or in groups of 2. If twopeople work together, make sure both people are listed as authors. Turn inthe technical report as a hard copy or in Assignments in Canvas.2y <- c(316.91, 325.68and so on, getting the other 5 mean co2 levels from the data file.With either method, as long as your variables arexandy, you are all setto fit a curve. First use the plot command to see what a scatter plot lookslike. The command for that isplot(y~x) .This puts the y-variable onthe vertical axis and the x-variable on the horizontal axes. Then (a) find thecorrelation coefficient ofxwithy.Then improve this correlation coefficient as much as possible using trans-formations in the familiesw←sqrt(y+c) andw←sqrt(y−c)wherecis a constant. You may limit your search to integer values ofc.(b) Give your highest correlation coefficient and give the transformation thatproduces it. (c) Regresswuponx(R function:lm(w~x)), and give theequation of the least squares line withwas the dependent variable andxasthe independent variable. (d) Solve the equation in part (c) foryin termsofx, and give the resulting equation. (e) Make a scatter plot of the original(x,y) data points, and superimpose the graph of the equation from part (d)on the scatter plot (R function:curve(f(x), add=TRUE).(f) If you entered the data by hand using 7 data points, give the atmo-spheric CO2 concentrations that your equation predicts for the years 2019and 2020.(f) If yourxandyvariables contain the full data lists from 1959 to 2020,give the atmospheric co2 concentrations predicted by your equation for theyears 2022 and 2023.Type up your results as an informative and short technical report. Usefull sentences. Your paper should occupy a little less than one side of a page,and it should be completely understandable to people who do not know whatthe assignment was. Include everything from parts (a) to (f) in your paper.You may sketch the scatter plot and superimposed curve by hand, or importit into your paper electronically. However, do not let it take up too muchspace!In typing up your report follow the Technical Report Guidelines postedin Canvas.
Technical Report Guidelines:
The Grey Literature International Steering Committee (GLISC), uses theterm “grey literature” for technical reports and other documents publishedby government agencies, universities, and other organizations not mainly inthe publishing business. The guidelines here are consistent with guidelinesset forth in 2005 by GLISC [1], but inconsistent with APA format whichoriginated in the 1920’s [2].A one-page technical report should be typed single spaced, using fullsentences. It should be only one page longand should contain the followingparts.•Title, author(s), date. This should all be in two or three lines centeredat the top of the page. A subtitle is optional.•Introduction, theory or question, methods, results, and conclusions.The source of the theory, question, or background information shouldbe indicated by reference to one or more of the references listed at theend of the paper. The results can include frequency tables, summarystatistics and graphs.•List of references. In a one-page technical report this list can havelength 1. Ideally the references should have the form “author(s), title,journal or publisher, year,” but in this internet age there are countlessvariations. In STAT 145, pretty much anything goes for reference for-mat and type, but references should be serious, not fictitious, and adate (or at least a year) should always be given.Since a one-page technical report must not exceed one page, the intro-duction must be brief, but is essential so that a general reader will knowwhat the heck the report is about! A general reader should be able to makesense out of everything. For example any tables or graphs must be referredto in the paper so a reader will know what they are. When conclusions arefrom hypothesis tests, they should be stated in full sentences with confidenceintervals or test statistics andP-values in parentheses.References: 1.Guidelines for the production of scientific and technical re-ports, GLISC, 2006.2.APA Style, Wikipedia, 2020.The Grey Literature International Steering Committee (GLISC), uses theterm “grey literature” for technical reports and other documents publishedby government agencies, universities, and other organizations not mainly inthe publishing business. The guidelines here are consistent with guidelinesset forth in 2005 by GLISC [1], but inconsistent with APA format whichoriginated in the 1920’s [2].A one-page technical report should be typed single spaced, using fullsentences. It should be only one page longand should contain the followingparts.•Title, author(s), date. This should all be in two or three lines centeredat the top of the page. A subtitle is optional.•Introduction, theory or question, methods, results, and conclusions.The source of the theory, question, or background information shouldbe indicated by reference to one or more of the references listed at theend of the paper. The results can include frequency tables, summarystatistics and graphs.•List of references. In a one-page technical report this list can havelength 1. Ideally the references should have the form “author(s), title,journal or publisher, year,” but in this internet age there are countlessvariations. In STAT 145, pretty much anything goes for reference for-mat and type, but references should be serious, not fictitious, and adate (or at least a year) should always be given.Since a one-page technical report must not exceed one page, the intro-duction must be brief, but is essential so that a general reader will knowwhat the heck the report is about! A general reader should be able to makesense out of everything. For example any tables or graphs must be referredto in the paper so a reader will know what they are. When conclusions arefrom hypothesis tests, they should be stated in full sentences with confidenceintervals or test statistics andP-values in parentheses.References: 1.Guidelines for the production of scientific and technical re-ports, GLISC, 2006.2.APA Style, Wikipedia, 2020.