CONCEPTS SEC MATH
CONCEPTS SEC MATH EMAT 3500
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This 6 page Class Notes was uploaded by Shirley Spencer on Saturday September 12, 2015. The Class Notes belongs to EMAT 3500 at University of Georgia taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/202325/emat-3500-university-of-georgia in Mathematics Education at University of Georgia.
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Date Created: 09/12/15
Chapter 4 Analyzing Bivariate Data with Fathom Chapter 4 Analyzing Bivariate Data with Fathom Summary Building from ideas introduced in Chapter 3 teachers continue to analyze automobile data using Fathom to look for relationships between two quantitative attributes They use the concept of variation and deviations from the mean in each univariate attribute to help conceptualize correlation and least squares regression as ways of describing the relationship in the bivariate data and developing a linear model for making predictions The teachers will consider pedagogical issues concerning the dif culties students may have in analyzing bivariate data and the bene ts and drawbacks for using conceptual underpinnings from univariate analysis to develop bivariate analysis techniques Objectives Mathematical Teachers will be able to 0 use concepts and techniques used in univariate data analysis to understand how two attributes covary and the techniques used to analyze two quantitative variables in bivariate data analysis describe how to create a linear model using the method of least squares describe the strength of the relationship between two quantitative attributes using correlation coef cient 0 analyze the appropriateness of a linear function as a model for a bivariate data using a residual plot 0 use the coef cient of determination to explain the amount of variation for a predicted value that can be attributed to a domain value by a least squares line 0 determine whether a linear function is an appropriate model for a set of data Technological Teachers will be able to use Fathom to 0 create box plots and scatterplots 0 plot functions and values on graphs 0 create a movable line and show squares 0 create a leastsquares lineofbest t 0 create a residual plot enter formulas 0 use the summary table to compute statistical measures Pedagogical Teachers will 0 discuss the bene ts and drawbacks related to different representations of data using dynamic les to conceptualize correlation and linear models 0 become familiar with some dif culties students have with creating and using a least squares linear model 0 consider bene ts and drawbacks of using tasks to assist students in reasoning about how to use univariate data analysis techniques to develop a better understanding of bivariate data analysis techniques Prerequisites univariate analysis techniques understanding mean and standard deviation as measures of center and spread dot plots and box plots Vocabulary covariation bivariate data scatterplot predictor variable response variable correlation coef cient residuals Sum of squares Least Squares regression line coef cient of determination interpolation extrapolation in uential points Learning to Teach Mathematics with Technology An Integrated Approach Page 67 Module One Data Analysis and Probability Draft Modified 972007 Chapter 4 Analyzing Bivariate Data with F alham Technology Files 2006Vehiclesftm Correlationftm Outlierftm Emergency Technology Files 2006Vehicles7Ch4Sect3 m 2006VehiclesiCh4Sect4 m 2006Vehicles Ch4Sect5ftm 2006Vehicles Ch4Sect6ftm Required Materials Fathom v 2 Learning to Teach Mathematics with Technology An Integrated Approach Page 68 Module One Data Analysis and Probability Draft Modified 972007 Chapter 4 Analyzing Bivariate Data with F atham Chapter 4 Analyzing Bivariate Data While measures of center and spread provide us with important information about the distribution of a single variable often more than one variable is collected and relationships between two or more variables are examined In Chapter 3 we used two attributes in the 2006 Vehicle data to answer a question about vehicles with which engine type seemed to have the best City mpg performance To answer that question we were using bivariate data with one quantitative attribute City mpg and one qualitative attribute Engine type Bivariate data is the term used to describe data that have two variables for each observation In this lesson we will focus on ways to examine relationships between two quantitative attributes When examining two quantitative measures in a data set our attention is on how the measures covary Thus for bivariate data covariation involves correspondence of the variation possible in each variable To help students conceptualize covariation we are going to build on what they already know about partitioning data sets and using measures of center and spread to describe univariate distributions Learning to Teach Mathematics with Technology An Integrated Approach Page 69 Module One Data Analysis and Probability Draft Modified 972007 your goals is to investigate the effects of changing data the Collection menu ect ea in a graph c ick y white Tech T To desel ses 39 1 Chapter 4 Analyzing Bivan39ate Data with Fathom Section 1 Examining Relationships Between Two Quantitative Variables Open the 2006Vehicleftm le and clear all previous graphs There are several quantitative attributes in this data set When considering a purchase ofa new vehicle a buyer is likely interested in the gas mileage for both city and highway When looking at the 2006 vehicle data we can ask the question Is there a relationship between City mpg and Hwy mpg for t is set 0 f vehicles We can begin by examining the distributions of the City mpg and the Hwy mpg on separate dot plots Drag down two empty Graph objects and create dot plots for each attribute 2on5 Vehicles 2 EVEmcles o o o c on o e v 00 o co co gogfefg 02 o 8 3033 eg a omowwm o 90 wvowowo lt70 0 o o n H 2D 30 an an EU 7n a ll 23 30 4o 50 60 7D City Hwy Figure 4 1 We can utilize Fathom s linked representations to informally investigate the nature of the relationship between the o distributions by selecting a portion of the cases in the City distribution and noticing the corresponding position of those cases in the Hwy distribution To select a portion of cases in a graph 1 in the graph window click and drag to draw a N o 1 E o E o L m a G i i o 33 o p E o m i o 8 a points will appear red in the raph However because the representations are all linked the same cases will be highlighted in all other open representations ofthis data Learning to Teach Mathem ti 5 with Te hnology An Integrated Approach a c c Page 70 Module one Data Analysis and Probability Dra Modi ed 972007 Chapter 4 Anaiyzrng Brvanate Data wrth FaLham ZUUE VEH E ES DmPM 3 2D EVEWE ES mem Q El 1U 2U 3U 4U 5U 6U 7U El 1U 2U 5U 6U 7D Figure43 FOCUS ON MATHEMATICS Q1 natw mpgandHWympg QL a a r represented by these points Q3 uu Lu Au a Click ofthe hn nlm 39 39 39 different parts of a box plot What do you notice Anya nut Q4 made in Q2 FOCUS ON PEDAGOGY pun u r quantitative attributes see 39339 Page 71 Module one Data Anaiysrs and Probabrhty Dratt Modi ed 972007
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