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Linear Regression

Linear Regression. Section 3.3. Warm Up.

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Linear Regression

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  1. Linear Regression Section 3.3

  2. Warm Up • In many communities there is a strong positive correlation between the amount of ice cream sold in a given month and the number of drownings that occur in that month. Does this mean that ice cream causes drowning? If not, can you think of other alternatives for the strong association?

  3. Warm Up #2…… • Explain why one would expect to find a positive correlation between the number of fire engines that respond to a fire and the amount of damage done in the fire.

  4. If the value of the correlation coefficient is significant, the next step is to find the equation of the regression line. Regression Line – The data’s line of best fit which is determined by the slope and y-intercept. Regression Line……

  5. It finds the equation of the line that best describes the relationship between the 2 variables. Primary Purpose: To Make Predictions *This is a test question. Regression Analysis……

  6. Prediction Models……

  7. The slope intercept form of a line was y = mx + b where m is the slope and b is the y-intercept Slope: The change in y over the change in x. Y-intercept: where the line crosses the y-axis. Remember Algebra?......

  8. The equation used to find the line of best fit is y = ax + b where “a” = slope and “b” = y-intercept Line of Best Fit……

  9. To find a: To find b: Computational Formulas……y = ax + b

  10. Example 1…… • Find the equation of the line of best fit. • Predict the # of sales when 5 ads are sold.

  11. Go by the formula……These are the lists you will need.

  12. Find the mean of x and the mean of y and write it down. Put x’s in L1 – stat calc one var stats L1 Put y’s in L2 – stat calc one var stats L2 First……

  13. Means of x and y……

  14. Let’s fill in the lists……

  15. Compute “a”……

  16. Compute “b”……

  17. Plug into y = ax + b…… • Answer: y = 1.16x + 2.8

  18. Predict …… • Predict the number of sales when 5 ads are sold. Y = 1.16(5) + 2.8 = 8.6 = 9 sales

  19. Example 2…… • A. Find the equation of the line of best fit. • B. Predict hours of exercise if the person is 35 yrs old. • C. Predict the age if they exercise 9 hours per week.

  20. X-Values: Y-Values: Find the means……

  21. The lists……

  22. Compute “a” and “b”……

  23. Equation: y = mx + b • Plug into the formula for the equation of the trend line. Y = -.18x + 10.50

  24. Find y when x = 35. Y = -.18(35) + 10.50 Y = 4.2 hours Find x when y = 9. 9 = -.18x + 10.50 9-10.50 = -.18x -1.5 = -.18x X = 8.3 X = 8 years Predictions……

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