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Warm up

Warm up. Find the equation of the line that goes through the two points y - y 1 = m(x - x 1 ) (2,6) (4,10 ) (1, 6) ( 3, -2). review. New Terms. Interpolation – estimating a value between known values Extrapolation – predicting a value outside of known values

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Warm up

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  1. Warm up Find the equation of the line that goes through the two points y - y1 = m(x - x1) (2,6) (4,10) (1, 6) ( 3, -2)

  2. review

  3. New Terms Interpolation – estimating a value between known values Extrapolation – predicting a value outside of known values line of best fit – A line that closely fits the data provided (kind of like the trend line from before) Linear Regression – a process of finding the least squares line (using our calculator)

  4. Interpolation vs. extrapolation Predict the income for 1982 Would this be interpolation or extrapolation? Predict the income for 2012 Would this be interpolation or extrapolation?

  5. Interpolation vs. extrapolation Predict the sales for day 17 Would this be interpolation or extrapolation? Predict the sales for day 8 Would this be interpolation or extrapolation?

  6. Line of best fit • Graph the following points and find an equation that would match the data

  7. Graphing Calculator

  8. Type in the data

  9. Correlation Coefficient • Correlation coefficient • Is a number between -1 and 1 describing how good of a match the linear regression equation is to the data presented. • if R = 1 or -1 it is a perfect match • if R is far from 1 or -1 it is not a very good match

  10. Diagnostic On

  11. Find the equation through the points

  12. Find the equation through the pointswhat is the correlation coefficient?

  13. Plotting Points

  14. Graphing the line with the points

  15. Graph the datafind the equationfind the correlation coefficientPredict the value when x = 7

  16. Graph the data and answer the questions • What is the slope of the line of best fit? • What does the slope mean in terms of the number of video and computer games sold per year? • What would you predict for the year 2008?

  17. Graph the data and answer the questions What would you predict the male population would be in 2007? What would you predict the male population would be in 2075? Do you feel that this would be an accurate estimation?

  18. Real World Problem Jill walks forward while Bob records her distance from where she started at one second intervals. The data recorded are listed to the right • Graph the data • Which time interval is Jill not moving? • Which time interval is Jill moving the fastest?

  19. Real World Examples Here's a graph used by a psychologist. Patients were asked to complete a series of personality tests; their answers were scored and each person was assigned a pair of numbers representing their self esteem and their likelihood of avoiding contact with other people. The graph shows a very weak negative correlation, indicating that people with high self esteem tend not to avoid interacting with others (or conversely, people with low self esteem avoid interpersonal contacts). This graph was used to by weather forecasters to compare temperature predictions with the temperatures that actually occurred, to gauge the accuracy of their predictions. The fact that the data points show a strong correlation indicates that the predictions were fairly good.

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