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Understanding Scatter Plots and Prediction Equations

Utilize scatter plots and prediction equations to analyze data and make predictions. Learn how to interpret correlations and create regression lines. Practice writing linear equations and predicting outcomes based on real-world examples.

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Understanding Scatter Plots and Prediction Equations

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 2–4) CCSS 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. Write an equation in slope-intercept form for theline with slope = , passing through (0, 1). A. B. C. D. 5-Minute Check 1

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

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

  9. Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Mathematical Practices 4 Model with mathematics. 5 Use appropriate tools strategically. CCSS

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

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

  12. Concept

  13. 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

  14. 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

  15. Slope formula Substitute. Simplify. Use a Scatter Plot and Prediction Equation B. Use two ordered pairs to write a prediction equation. Find an equation of the line through (3, 18) and (15, 13). Begin by finding the slope. Example 1B

  16. Point-slope form Substitute. Distributive Property Simplify. Answer: One prediction equation is Use a Scatter Plot and Prediction Equation 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. Example 1A

  21. A. B. C. D. B.The scatter plot shows 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. C.The equation represents the approximate percent of drivers y who wear seat belts in various years x 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. D. How accurate is the prediction about the percent of drivers who will wear seat belts in 2010? 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. End of the Lesson

  25. Page 96, 98 #3 – 6, 23 – 25, 30, 32

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