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Statistics: Scatter Plots and Lines of Fit
Lesson 5-7 Statistics: Scatter Plots and Lines of Fit
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Objectives Interpret points on a scatter plot
Write equations for lines of fit
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Vocabulary Scatter plot – Two sets of data plotted as ordered pairs in a coordinate plane Positive correlation – in a scatter plot, as x increases, y increases line of fit – a line that describes the trend of the data in a scatter plot Best-fit line – The line that most closely approximates the data in a scatter plot Linear interpolation – The use of a linear equation to predict values that are inside of the data range Negative correlation – in a scatter plot, as x increases, y decreases
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x-y Coordinate Plane Point Plotting Quadrants II I III IV
up 7 left 4 right 5 III IV down 8 (x, y) (-4, 7) (5, -8) x – left or right y – up or down
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Example 1a Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows average personal income for U.S. citizens. Answer: The graph shows a positive correlation. With each year, the average personal income rose.
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Example 1b Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows the average students per computer in U.S. public schools. Answer: The graph shows a negative correlation. With each year, more computers are in the schools, making the students per computer rate smaller.
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Population (millions)
Example 2a The table shows the world population growing at a rapid rate. Year Population (millions) 1650 500 1850 1000 1930 2000 1975 4000 1998 5900 Draw a scatter plot and determine what relationship exists, if any, in the data and draw a line of fit.
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Example 2a cont Let the independent variable x be the year and let the dependent variable y be the population (in millions). The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables. Draw a line of fit for the scatter plot. No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot.
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Example 2b Write the slope-intercept form of an equation for equation for the line of fit. The line of fit shown passes through the data points (1850, 1000) and (1998, 5900). Step 1 Find the slope. Slope formula Let and Simplify.
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Example 2b cont Step 2 Use m = 33.1 and either the point-slope form or the slope-intercept form to write the equation. You can use either data point. We chose (1850, 1000). Point-slope form Slope-intercept form Answer: The equation of the line is
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Example 3 Use the prediction equation y ≈ 33.1x – 60,235 where x is the year and y is the population (in millions), to predict the world population in 2010. Original equation Replace x with 2010. Simplify. Answer: 6,296,000,000
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Summary & Homework Summary: Homework:
If y increases as x increases, then there is a positive correlation between x and y If y decreases as x increases, then there is a negative correlation between x and y If there is no relation between x and y, then there is no correlation between x and y A line of fit describes the trend of data You can use the equation of a line of the fit to make predictions about the data Homework: N/A 3 graphs
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