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Warm Up

Warm Up. Go ahead and start wrapping up your Guess My Age projects. Discuss methods with other members in your group. “Fine Tune” anything you need to change. A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient.

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Warm Up

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  1. Warm Up • Go ahead and start wrapping up your Guess My Age projects. • Discuss methods with other members in your group. • “Fine Tune” anything you need to change.

  2. A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. • Find the correlation coefficient & interpret it. • Find & interpret the slope. • Find & interpret the y-intercept. • Give the least squares regression line.

  3. Correlation & Regression – Non Linear Emphasis

  4. Objective Find prediction equations for linear, quadratic, and exponential models.

  5. Relevance To be able to find an equation to best represent quantitative data with 2 variables and use it to make predictions and to understand slope and y-intercept in context of the problem.

  6. Non Linear

  7. Positive Quadratic Regression: Negative Quadratic Regression: Non Linear Regression Shapes……

  8. Positive Exponential Regression: Negative Exponential Regression: Non Linear Regression Shapes……

  9. Quadratic: Exponential: Quadratic and Exponential on Calculator……

  10. What should you look for to tell if it is not linear?...... • Sometimes a high “r” value for linear regression is deceptive. You must look at the scatter plot AND you must look at the residual pattern it makes. • Residuals – positive and negative deviations from the least squares line. Each residual is the difference between the observed y value and the corresponding predicted y value. • If the residuals have a curved pattern then it is NOT linear.

  11. Residuals • Variation in the y values can be effectively explained when the residuals are small – close to the line. • Remember Residual = observed – predicted

  12. Residual Plot

  13. Scatter Plot vs. Residual Plot

  14. Height vs Shoe size – residual plot Good residual plot – shows relatively no pattern.

  15. Good or Bad (Residual Plot Shown) Not Linear Linear

  16. Notice • A residual plot in effect turns the regression line horizontal. • It magnifies the deviations of the points from the line, making it easier to see unusual observations and patterns. • That is why if the regression line captures the overall pattern of the data, there should be NO pattern in the residuals!

  17. Example……The scatter plot could possibly be linear. You must check the residual pattern.

  18. Change y-list to residsafter running a linear correlation regression – 2nd stat resid: Notice the curved pattern in the residuals. It is either quadratic or exponential. Resids: 2nd Stat

  19. Equation: This is a quadratic regression…..

  20. Example 2……Is it linear?

  21. There is acurved pattern in the residuals. It is NOT linear – we will see that it is exponential. (Positive) Look at the residuals……

  22. Here is the equation you should use for predictions:

  23. Practice Assignment…… • Worksheet

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