CONSTRUCTING FUNCTIONS FROM REAL WORLD DATA



Notes on CONSTRUCTING FUNCTIONS FROM REAL WORLD DATA by Mary Ann TuerkI always introduce in College Algebra the writing of functions for real world data by using the TI-84’s ability to create SCATTER PLOTS and FINDING THE LINE OF BEST FIT (REGRESSION EQUATIONS).The Blitzer text introduces these concepts in Sec 2.3 so you can fit this in anytime after that. I usually wait until after Sec 3.1 on quadratic functions since the lab uses Quadratic Regression models.Since most students are not familiar with the concept of curve fitting or with the STAT menu, I usually do Case I and Case II as an inclass exercise. (I plan to update Case I and use Example 9 (p.238) on Carbon dioxide and Global Temperature ). Then I assign the lab on MRSA data as a graded lab.MTH 112 College Algebra/TuerkCONSTRUCTING FUNCTIONS FROM REAL WORLD DATAWhen we gather real world data, we often first arrange the data in a table format. In many applications, time is the independent variable and we are monitoring how some other quantity changes over time.Next we might want to graph the data as a set of points on the coordinate plane. Data presented in visual form as a set of discrete (unconnected) points is called a scatter plot. Finally after observing the pattern of the data, we want to find an equation that shows the relationship between the variables. If the relationship is best described by a linear function, we call the process finding the line of best fit or finding the regression line. If the relationship is best described by a curve, we call the process curve fitting.In this lab, we will see how a graphing calculator can be used for all of the above: to enter the data in a table (via lists); to create a scatter plot; and to determine the regression function.This lab has two parts. Part I will be substantially completed in class today and Part II, the graded lab, will completed outside of class.IN CLASS LABCase I: Data on The Graying of America (from Blitzer 4th ed)Year1970198019902000 MedianAge27.930.032.835.3 Enter the data in two lists (STAT menu) of your calculator. In L1, enter the year; we will scale the data and use the number of years since 1970. In L2, enter the Median Age.Set an appropriate window for the data.Go to STAT PLOT (2nd Y= )and turn on Plot 1. Draw below and label the scatter plot of the data.Use the linear regression on your graphing calculator to find the line of best fit (the regression equation). (STAT/ CALC/4:Lin Reg L1,L2,Y1). Write the equation below.Y = ________________Graph the regression equation on the scatter diagram (on your calculator) and copy on your drawn graph above.How good a fit is the line to the data? Explain your reasoning.Use the equation to predict what the median age will be in 2010.________________INCLASS LAB - CONTINUEDCASE II: Medicare Spending in the US from 1995 to 2005. (From Blitzer 4th ed)Choosing the best model. Year19951996199719981999200020012002200320042005Spending(Billions)178199219240263288315345379416458Enter the data from the table into L3 and L4 in your graphing calculator. Scale the years to be the number of years after 1995.Create a scatter plot in the appropriate window.Use the regression options under STAT CALC to find two different models for the data.The Linear Regression : Y= ____________________The Quadratic Regression: Y= __________________ 4. Use both models to predict the Medicare spending in 2010:Linear Model: __________Quadratic Model:___________5. Which model do you think is better? What factors would influence your choice of model? Answer in complete sentences. MTH 112 – LAB ON REGRESSION20 pointsDUE: This week several states reported increases in the number of cases of antibiotic resistant staph infections, also known as MRSA. This potentially fatal infection was previously known as a risk for patients in hospitals; now it is showing up in community based situations, such as members of a high school football team in Virginia.The following data shows the increased number of cases in England and Wales in which MRSA was listed on death certificates as the underlying cause of death. (source: .uk)Year1993949596979899200020012002200320042005Number Of Cases1711692613123433803945396906588149091108 1. Enter the data into lists in your calculator. Create a scatter plot of the data. Carefully copy the scatter plot onto a separate sheet of paper. You may want to use graph paper. Be sure your axes are labeled with numerical scales and titles.2. Use the regression equation feature of your graphing calculator to explore at least three models for the data. Show the results as equations below. 3. For each of the three models, what is the expected number of deaths from MRSA in 2010?4. Which model do you think is the best choice and why? Answer in complete sentences. Graph this equation over your data on your paper. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download