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Scatter Plots

Scatter Plots. A graph of a set of data pairs (x, y). Correlation Coefficient, r. A number, denoted by r , from -1 to 1 that measures the strength and direction of a linear relationship between two variables. 3 Types of Correlation. Positive Negative No Correlation.

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Scatter Plots

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  1. Scatter Plots A graph of a set of data pairs (x, y)

  2. Correlation Coefficient, r A number, denoted by r, from -1 to 1 that measures the strength and direction of a linear relationship between two variables

  3. 3 Types of Correlation Positive Negative No Correlation

  4. Positive Correlation Relationship between paired data when y tends to increase as x increases

  5. Negative Correlation Relationship between paired data when y tends to decrease as x increases

  6. No Correlation (or Zero Correlation) The points do not lie close to any line

  7. Strong Positive Correlation The points are clustered resembling a rising straight line with a positive slope.r is close to +1 http://www.regentsprep.org/regents/math/algebra/AD4/scatter.htm

  8. Weak Positive Correlation Points tend to rise, but this is a weak positive slope

  9. Strong Negative Correlation The points are clustered resembling a falling straight line with a negative slope.r is close to -1

  10. Weak Negative Correlation Points tend to fall, but this is a weak negative slope

  11. No way to determine and no straight line forms

  12. 1. The scatter plot shows a relationship between hours worked and money earned. Which best describes the relationship between the variables? Strong Positive Correlation

  13. 2. The scatter plot shows a relationship between age and height. Which best describes the relationship between the variables? No Correlation

  14. 3. The scatter plot shows a relationship between age of a car and its value. Which best describes the relationship between the variables? Weak Negative Correlation

  15. 4. The scatter plot shows a relationship between number of customers and the temperature.Which best describes the relationship between the variables? Weak Positive Correlation

  16. Some Types of Regression Linear Regression -straight line form

  17. Some Types of Regression Quadratic Regressionparabolic form (u-shape)

  18. Linear Regression A method for finding the equation of the best-fitting line,

  19. 1. Which choice is the best example of a line of best fit?

  20. 2. Matt considers whether or not the amount of time students study for a test are related. He determines that the more they study the higher grade they will get. What type of slope would the line of best fit have? • negative • positive • undefined • zero

  21. 3. What type of model best describes this data’s relationship? • Linear • Quadratic • Exponential • No relationship Hint: look at the rate of increase…is it constant?

  22. 4. What type of model best describes this data’s relationship? • Linear • Quadratic • Exponential • No relationship Hint: look at the rate of increase

  23. 5. What type of model best describes this data’s relationship? • Linear • Quadratic • Exponential • No relationship

  24. 6. The graph shows Jessica’s weight as it compares to her age. Using the line of best fit, what is the best approximation for her weight at age 9 • 70 • 75 • 80 • 85

  25. 7. The table shows the average household size y in the U.S. from 1930 to 2000. y = -.021t + 3.9425 Use the model and predict the average household size in 2030. (2030 – 1930) and substitute that in for t 1.84

  26. Consumer Debt The table shows the total outstanding consumer debt (excluding home mortgages) in billions of dollars in selected years. (Data is from the Federal Reserve Bulletin.) Let x = 0 correspond to 1985. The best fit line is

  27. 8. Find the approximate consumer debt in 1998. 9. Find the approximate consumer debt in 2008. 1501.517 billion 2300.107 billion

  28. Health The table below shows the number of deaths per 100,000 people from heart disease in selected years. (Data is from the U.S. National Center for Health Statistics.) Let x = 0 correspond to 1960. The line of best fit is

  29. 10. Find an approximation for the number of deaths due to heart disease in 1995. 11. Predict the number of deaths from heart disease in 2008. 293 193 almost 194

  30. 12. Which equation best fits the scatterplot?

  31. 13. Which equation best fits the scatterplot?

  32. 14. Which equation best fits the scatterplot?

  33. 15. What type of model would best fit the data? • Linear • Quadratic • Exponential • Cubic

  34. 16. What type of model would best fit the data? • Linear • Quadratic • Exponential • Cubic

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