- Fit data to quadraticmodels.
- Fit data to trigonometricmodels.
- Fit data to exponentialgrowthand decaymodels.
Introduction
In our last lessonwe examinedfunctionsand learnedhow to classifyand sketchfunctions.In this lesson
we will use someclassicfunctionsto modeldata.The lessonwill be a set of examplesof eachof the models.
For each,we will makeextensiveuse of the graphingcalculator.
Let’s do a quickreviewof how to modeldata on the graphingcalculator.
EnterDatain Lists
Press[STAT]and then[EDIT]to accessthe lists,L1–L6.
View a ScatterPlot
Press 2 nd [STAT PLOT]and chooseaccordingly.
Thenpress[WINDOW]to set the limitsof the axes.
Computethe RegressionEquation
Press[STAT]then choose[CALC]to accessthe regressionequationmenu.Choosethe appropriateregres-
sion equation(Linear, Quad,Cubic,Exponential,Sine).
Graphthe RegressionEquationOverYour ScatterPlot
Go toY=>[MENU]and clearequations.Press[VARS], then enter 5 andEQand press[ENTER](Thisseries
of entrieswill copythe regressionequationto yourY =screen.)Press[GRAPH]to viewthe regression
equationover your scatterplot
Plottingand Regressionin Excel
You can also do regressionin an Excelspreadsheet.To start,copyand pastethe tableof data into Excel.
Withthe two columnshighlighted,includingthe columnheadings,click on theCharticon and selectXY
scatter. Acceptthe defaultsuntil a graphappears.Selectthe graph,then clickChart, thenAdd Trendline.
Fromthe choicesof trendlineschooseLinear.
Now let’s beginour surveyof the variousmodelingsituations.
LinearModels
For thesekindsof situations,the data will be modeledby the classiclinearequation Our task
will be to find appropriatevaluesof and for givendata.
Example1:
It is said that the heightof a personis equalto his or her wingspan(the measurementfrom fingertipto fin-
gertipwhenyour armsare stretchedhorizontally).If this is true, we shouldbe able to take a tableof mea-
surements,graphthe measurementsin an coordinatesystem,and verifythis relationship.Whatkind
of graphwouldyou expectto see?(Answer:You wouldexpectto see the pointson the line .)