Alg 1 5.4 pg 296

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GOAL 2DETERMINING THE CORRELATION OF X AND YCorrelation is a number r satisfying º1 ≤ r ≤ 1 that indicates how well aparticular set of data can be approximated by a straight line. The Activity onpage 299 shows how to find an r-value using a calculator. In this course you willdescribe a correlation without actually finding r-values, as described below.When the points on a scatter plot can be approximated by a line with positiveslope, x and y have a positive correlation. When the points can be approximatedby a line with negative slope, x and y have a negative correlation. When thepoints cannot be well approximated by a straight line, we say that there isrelatively no correlation.yyyxxxPositive correlation Negative correlation Relatively no correlationEXAMPLE 3Using CorrelationIn swimming events, performance is positively correlated with time.a. The two graphs show the winning 100-meter women’s freestyle swimmingtimes and the winning women’s long jump distances for the Olympics from1948 through 1996. Which is which? Explain your reasoning.b. Describe the correlation of each set of data.FOCUS ONAPPLICATIONS1948195619641972Year1980198819961948195619641972Year198019881996 Source: Information Please Almanac Source: Information Please AlmanacFREESTYLESWIMMING In afreestyle swimming event,the swimmer can choosethe stroke. Usually, theswimmer chooses theAustralian Crawl.APPLICATION LINKwww.mcdougallittell.comREALINTERNETLIFESOLUTIONa. The first graph must represent the long jump distances because the winnershave tended to jump farther with each Olympic year. The second graph mustrepresent the swimming times because the winners have tended to swimfaster with each Olympic year, so their times have been decreasing.b. The first graph shows a positive correlation between the year and the winningdistance. The second graph shows a negative correlation between the yearand the winning time.5.4 Fitting a Line to Data 295
GUIDED PRACTICEVocabulary Check ✓Concept Check ✓Skill Check ✓1. The line that most closely fits a set of data is called the ? .Draw a scatter plot of data that have the given correlation.2. Positive 3. Negative 4. Relatively no5. DISCUS THROWS Predict the distance of the winning throw in theyear 2005 from the data in Example 2. Explain your reasoning.Draw a scatter plot of the data. State whether x and y have a positivecorrelation, a negative correlation, or relatively no correlation. If possible,draw a line that closely fits the data and write an equation of the line.6. x y 7. x y 8. x y 9.1 2º3 81.1 5.12 9º2 61.7 5.53 8º1 52.2 5.94 10 32.6 6.35 41 23.3 7.56 82 03.5 7.6x y5.5 0.46.2 1.07.7 2.58.1 2.99.2 4.39.7 5.5PRACTICE AND APPLICATIONSSTUDENT HELPExtra Practiceto help you masterskills is on p. 801.FITTING LINES Copy the graph and draw a line that corresponds closely tothe data. Write an equation of your line.10. y11. y 12.y3111113 x31131 x1 1 3 x1FITTING LINES Draw a scatter plot of the data. Draw a line thatcorresponds closely to the data and write an equation of the line.STUDENT HELPHOMEWORK HELPExample 1: Exs. 10–16,23Example 2: Exs. 10–16,23Example 3: Exs. 17–2213. x y 14. x y 15. x y 16.1.0 3.8 3.0 7.1 3.0 9.91.5 4.2 3.4 8.1 3.5 9.71.7 5.3 4.0 8.5 3.7 8.62.0 5.8 4.1 8.9 4.0 8.12.0 5.5 4.8 9.6 4.0 8.41.5 6.7 5.2 9.8 4.5 7.4x y5.0 6.85.4 5.86.0 5.66.1 5.26.8 4.37.2 3.5296 Chapter 5 Writing Linear Equations
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Alg 1 5.4 pg 296

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