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Scatter Plots and Prediction Equations for Real-World Data

Learn how to create scatter plots, find regression lines, and make predictions using prediction equations for real-world data.

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Scatter Plots and Prediction Equations for Real-World Data

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 2–4) Then/Now New Vocabulary Key Concept: Scatter Plots Example 1: Real-World Example: Use a Scatter Plot and Prediction Equation Example 2: Real-World Example: Regression Line Lesson Menu

  3. A B C D Write an equation in slope-intercept form for theline with slope = , passing through (0, 1). A. B. C. D. 5-Minute Check 1

  4. A B C D Write an equation in slope-intercept form for theline with slope = –1, passing through A. B. C. D. 5-Minute Check 2

  5. A B C D A.4x + 8y – 11 = 0 B.y = 4x – 11 C. D. What is the slope-intercept form of 4x + 8y = 11? 5-Minute Check 3

  6. A B C D Write an equation in slope-intercept form of a line that passes through (1, 1) and (0, 7). A. 6x – y = 7 B.y = –6x + 7 C.x – 7y = 1 D.y = x + 7 5-Minute Check 4

  7. A B C D A plumber charges a flat fee of $65, and an additional $35 per hour for a service call. Write an equation that represents the charge y for a service call that lasts x hours. A.y = 35x + 65 B. 65 = 35x + y C.y = 65x + 35 D. total = 35x + 65y 5-Minute Check 5

  8. A B C D What is the equation of a line that passes through the point (6, –4) and is perpendicular to the equation A. e B. e C. e D. e 5-Minute Check 5

  9. You wrote linear equations. • Use scatter plots and prediction equations. • Model data using lines of regression. Then/Now

  10. bivariate data • regression line • correlation coefficient • scatter plot • dot plot • positive correlation • negative correlation • line of fit • prediction equation Vocabulary

  11. Concept

  12. Use a Scatter Plot and Prediction Equation A. EDUCATIONThe table below shows the approximate percent of students who sent applications to two colleges in various years since 1985. Make a scatter plot of the data and draw a line of fit. Describe the correlation. Example 1A

  13. Use a Scatter Plot and Prediction Equation Graph the data as ordered pairs, with the number of years since 1985 on the horizontal axis and the percentage on the vertical axis. The points (3, 18) and (15, 13) appear to represent the data well. Draw a line through these two points. Answer:The data show a strong negative correlation. Example 1A

  14. Slope formula Substitute. Simplify. Use a Scatter Plot and Prediction Equation B. Find a prediction equation. What do the slope and y-intercept indicate? Find an equation of the line through (3, 18) and (15, 13). Begin by finding the slope. Example 1B

  15. Point-slope form Substitute. Distributive Property Simplify. Use a Scatter Plot and Prediction Equation Example 1B

  16. Answer: One prediction equation is Use a Scatter Plot and Prediction Equation The slope indicates that the percent of students sending applications to two colleges is falling about 0.4% each year. The y-intercept indicates that the percent in 1985 should have been about 19%. Example 1B

  17. Prediction equation x = 25 Simplify. Use a Scatter Plot and Prediction Equation C.Predict the percent of students who will send applications to two colleges in 2010. The year 2010 is 25 years after 1985, so use the prediction equation to find the value of y when x = 25. Answer: The model predicts that the percent in 2010 should be about 8.83%. Example 1C

  18. Use a Scatter Plot and Prediction Equation D.How accurate is this prediction? Answer: Except for the point at (6, 15), the line fits the data well, so the prediction value should be fairly accurate. Example 1D

  19. A. SAFETYThe table shows the approximate percent of drivers who wear seat belts in various years since 1994. Which shows the best line of fit for the data? Example 1A

  20. A B C D A.B. C.D. Example 1A

  21. A B C D A. B. C. D. B.The table and scatter plot show the approximate percent of drivers who wear seat belts in various years since 1994. What is a good prediction equation for this data? Use the points (6, 71) and (12, 81). Example 1B

  22. A B C D C.The table and scatter plot show the approximate percent of drivers who wear seat belts in various years since 1994. Predict the percent of drivers who will be wearing seat belts in 2010. A. 83% B. 87% C. 90% D. 95% Example 1C

  23. A B C D D.The table and scatter plot show the approximate percent of drivers who wear seat belts in various years since 1994. How accurate is the prediction? A. There are no outliers so it fits very well. B. Except for the one outlier the line fits the data very well. C. There are so many outliers that the equation does not fit very well. D. There is no way to tell. Example 1D

  24. Regression Line INCOME The table shows the median income of U.S. families for the period 1970–2002. Use a graphing calculator to make a scatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the median income in 2015. Usea graphing calculator to make ascatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the attendance in 2015. Example 2

  25. Regression Line Step 1 Make a scatter plot. Enter the years in L1 and the income in L2. Set the viewing window to fit the data. Use STAT PLOT to graph the scatter plot. Step 2 Find the equation of the line of regression. Find the regression equation by selecting LinReg(ax + b) on the STAT CALC menu. The regression equation is about y = 1349.87x – 2,650,768.347. The slope indicates that the income increases at a rate of about 1350 people per year. The correlation coefficient r is 0.997, which is very close to 1. So, the data fit the regression line very well. Example 2

  26. Regression Line Step 3 Graph the regression equation. Copy the equation to the Y = list and graph. Notice that the regression line comes close to most of the data points. As the correlation coefficient indicated, the line fits the data well. Example 2

  27. Regression Line Step 4 Predict using the function. Find y when x = 2015. Use VALUE on the CALC menu. Reset the window size to accommodate the x-value of 2015. Answer: According to the function, the median income in 2015 will be about $69,220 people. Example 2

  28. A B C D The table shows the winning times for an annual dirt bike race for the period 2000–2008.Use a graphing calculator to make a scatter plot of the data. Find and graph a line of regression. Then use the function to predict the winning time in 2015. A.y = –15.75x + 31,890.25; about 154 seconds B.y = –14.75x + 29,825.67; about 104 seconds C.y = –14.6x + 29,604.72; about 186 seconds D.y = –14.95x + 30,233.25; about 99 seconds Example 2

  29. End of the Lesson

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