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Regression & Prediction

Regression & Prediction. Linear Regression . Finding the best fitting straight line for a set of data This line is represented by the equation Y = bX + a, where a & b are fixed constants. Y=bX+a. Least Squares Regression. Most commonly used regression line

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Regression & Prediction

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  1. Regression & Prediction

  2. Linear Regression • Finding the best fitting straight line for a set of data • This line is represented by the equation Y = bX + a, where a & b are fixed constants

  3. Y=bX+a Least Squares Regression • Most commonly used regression line • Makes the sum of the squared errors as small as possible Regression Line Equation • Y(hat) is the predicted value of Y given a certain X • b is the slope • a is the y-intercept

  4. Slope (b) • Indicates by how much Y will change when X is increased by one point

  5. Relationship of “b” to “r” • When “r” is positive, “b” is positive • When “r” is zero, “b” is zero • When “r” is negative, “b” is negative

  6. Y-Intercept (a) • Value of Y when X is equal to 0 a = MY - bMX

  7. How Good is Our Prediction - Standard Error of Estimate • Provides a measure of how accurately the regression equation predicts the Y values • Gives a measure of the standard distance between a regression line and the actual data points • Analogous to standard deviation.

  8. Standard Error of Estimate - Formula

  9. Another Formula for Standard Error of Estimate • SSerror=(1-r2)SSY • By using this formula for SSerror the standard error of estimate can also be computed as

  10. Example A professor claims that the scores on the 1st exam provide an excellent indication of how students will perform throughout the term

  11. Calculate SP

  12. Calculate SSx

  13. Calculate SSY

  14. Calculate r

  15. Calculate Regression Equation Y’ = bX+a a = MY - bMX

  16. Standard Error of Estimate

  17. Standard Error of Estimate

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