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Section 4.8 Line of Best Fit

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Let’s make a scatter plot on the board together. 1.) Think of how old you are in months, and your shoe size. 2.) Plot on the board your information. x-axis, age in months from 150 to 200 y-axis, show size 4 to 15 3.) Now think of a younger sibling and plot what you think is their information 4.) Is there a correlation? 5.) Can we make a prediction for someone 30 years old? 3 years old?

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Age (months) Height (inches) 1876.1 1977 2078.1 21 2278.8 2379.7 2479.9 2581.1 2681.2 2782.8 28 2983.5 Work with your group to make a prediction for the height at: 21 months 28 months 20 years

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Line of Best Fit Definition - A Line of Best is a straight line on a Scatterplot that comes closest to all of the dots on the graph. A Line of Best Fit does not touch all of the dots. A Line of Best Fit is useful because it allows us to: –Understand the type and strength of the relationship between two sets of data –Predict missing Y values for given X values, or missing X values for given Y values

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Equation For Line of Best Fit y = 0.6618x + 64.399 X (months)FormulaY (inches) 21 0.6618(21) + 64.399 28 0.6618(28) + 64.399 240 0.6618(240) + 64.399 78.3 82.9 223.3

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Use the data to predict how much a worker will earn in tips in 10 hours. Example 2: Try this According to the graph, a worker will earn approximately $24 in tips in 10 hours.

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Use the data to predict how many circuit boards a worker will assemble in 10 hours. Try This: Example 3 Course 3 Scatter Plots According to the graph, a worker will assemble approximately 12 circuit boards in 10 hours. Hours Worked 486911 Circuit Board Assemblies 275812 14 12 10 8 6 4 2 2 4 6 8 10 12 14 Hours Circuit Board Assemblies

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BIRD POPULATIONS The table shows the number of active woodpecker clusters in a part of the De Soto National Forest in Mississippi. Determine the correlation between the year and the number of Active clusters. Year 199219931994199519961997199819992000 Active clusters 222427 3440424551

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SOLUTION EXAMPLE 3 Make a scatter plot of the data. Let x represent the number of years since 1990. Let y represent the number of active clusters Since the dots are generally going up and to the right, we say this is a positive correlation.

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Describe the correlation of the data graphed in the scatter plot. The scatter plot shows a positive correlation between hours of studying and test scores. This means that as the hours of studying increased, the test scores tended to increase.

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EXAMPLE 1 Describe the correlation of data The scatter plot shows a negative correlation between hours of television watched and test scores. that as the hours of television This means that as the hours of television watched Increased, the test scores tended to decrease.

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Swimming Speeds EXAMPLE 2 The table shows the lengths (in centimeters) and swimming speeds (in centimeters per second) of six fish. a. Make a scatter plot of the data. b. Describe the correlation of the data.

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EXAMPLE 2 b. The scatter plot shows a positive correlation, which means that longer fish tend to swim faster. SOLUTION a. Treat the data as ordered pairs. Let x represent the fish length (in centimeters),and let y represent the speed (in centimeters per second). Plot the ordered pairs as points in a coordinate plane.

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GUIDED PRACTICE Make a scatter plot of the data in the table. Describe the correlation of the data. ANSWER The scatter plot shows a positive correlation.

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