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10-3 Regression

10-3 Regression. College Prep Stats. Regression. Definitions Regression Equation Given a collection of paired data, the regression equation: algebraically describes the relationship between the two variables. Regression Line (or line of least-squares)

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10-3 Regression

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  1. 10-3 Regression College Prep Stats

  2. Regression Definitions • Regression Equation • Given a collection of paired data, the regression equation: algebraically describes the relationship between the two variables. • Regression Line (or line of least-squares) • The graph of the regression equation

  3. Example

  4. The Regression Equation x is the independent variable (predictor variable) ^ y is the dependent variable (response variable) ^ b0 = y - intercept y = b0 +b1x b1 = slope y = mx +b

  5. Notation for Regression Equation Population Parameter Sample Statistic y-intercept of regression equation 0b0 Slope of regression equation 1b1 Equation of the regression line y = 0 + 1xy = b0 + b1

  6. Assumptions 1. We are investigating only linearrelationships. 2. For each x value, y is a random variable having a normal (bell-shaped) distribution. All of these y distributions have the same variance. Also, for a given value of x, the distribution of y-values has a mean that lies on the regression line. (Results are not seriously affected if departures from normal distributions and equal variances are not too extreme.)

  7. Formula for b0 and b1 (y) (x2) - (x) (xy) b0= (y-intercept) n(x2) - (x)2 n(xy) - (x) (y) b1 =(slope) n(x2) - (x)2

  8. Finding Equation on Calculator • Enter Data values in L1 and L2 • Go to STAT-CALC-LinReg (a+bx)

  9. Data from the Garbage Project x Plastic (lb) 0.27 2 1.41 3 2.19 3 2.83 6 2.19 4 1.81 2 0.85 1 3.05 5 y Household Calculator Example Construct the regression line for thefollowing data:

  10. Graph It

  11. Predictions In predicting a value of y based on some given value of x ... 1. If there is not a significant linear correlation, the best predicted y-value is . Use r from last section to determine correlation! 2. If there is a significant linear correlation, the best predicted y-value is found by substituting the x-value into the regression equation.

  12. Examples • Predict the tip on a bill of $75 • Predict the size of a family that discards 0.5 pounds of plastic per week • Predict the IQ of a 7 foot tall male.

  13. Homework • P.549: 15-18

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