Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Calculating the Regression Line Lecture 42 Section 13 3 2 Robb T Koether Hampden Sydney College Tue Apr 7 2009 Outline Calculating the Regression Line 1 Homework Review 2 Formulas for the Regression Line 3 The Regression Line on the TI 83 4 Interpolation and Extrapolation 5 Free Lunch vs Graduation Rate 6 Assignment Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Homework Review Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Exercise 13 2 page 821 Data were gathered to estimate the regression line for a model where a gymnast s score y depends on the gymnast s physical condition as measured by his or her weight x The estimated regression line is given by y 1190 1 9x Complete the following sentence Every additional pound that a gymnast weighs drops the predicted score by about points on average Homework Review Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Exercise 13 2 page 821 The slope 1 9 tells how fast y changes with respect to x That is the slope represents the change in y for an increase of 1 in x Therefore if a gymnast gains one pound then we expect his score to drop by 1 9 points The Least Squares Regression Line Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment The equation of the regression line is of the form y a bx b is the slope of the regression line a is the y intercept We need to find the coefficients a and b from the data The Least Squares Regression Line Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment The formula for b is P b x x y y P x x 2 The formula for a is a y bx The Least Squares Regression Line Calculating the Regression Line Example Strong Positive Association Robb T Koether Homework Review Formulas for the Regression Line Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment The Regression Line on the TI 83 The Least Squares Regression Line Calculating the Regression Line Example Weak Positive Association Robb T Koether Homework Review Assignment Free Lunch vs Graduation Rate The Regression Line on the TI 83 Interpolation and Extrapolation Formulas for the Regression Line The Least Squares Regression Line Calculating the Regression Line Example Strong Negative Association Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment The Least Squares Regression Line Calculating the Regression Line Example Weak Negative Association Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment The Least Squares Regression Line Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment An alternate formula for b is P P P n xy x y b P P n x2 x 2 This is the one that the TI 83 uses Example Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Example Calculating the Regression Line Consider again the data set x 1 3 4 5 8 9 11 15 y 8 12 9 14 16 20 17 24 x x y y x x 2 y y 2 x x y y Example Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Example Calculating the Regression Line Compute the x deviations x 1 3 4 5 8 9 11 15 y 8 12 9 14 16 20 17 24 x x 6 4 3 2 1 2 4 8 y y x x 2 y y 2 x x y y Example Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Example Calculating the Regression Line Compute the y deviations x 1 3 4 5 8 9 11 15 y 8 12 9 14 16 20 17 24 x x 6 4 3 2 1 2 4 8 y y 7 3 6 1 1 5 2 9 x x 2 y y 2 x x y y Example Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Example Calculating the Regression Line Compute the squared x deviations x 1 3 4 5 8 9 11 15 y 8 12 9 14 16 20 17 24 x x 6 4 3 2 1 2 4 8 y y 7 3 6 1 1 5 2 9 x x 2 36 16 9 4 1 4 16 64 y y 2 x x y y Example Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Example Calculating the Regression Line Compute the squared y deviations x 1 3 4 5 8 9 11 15 y 8 12 9 14 16 20 17 24 x x 6 4 3 2 1 2 4 8 y y 7 3 6 1 1 5 2 9 x x 2 36 16 9 4 1 4 16 64 y y 2 49 9 36 1 1 25 4 81 x x y y Example Calculating the Regression Line Robb T Koether Homework Review Formulas for the Regression Line The Regression Line on the TI 83 Interpolation and Extrapolation Free Lunch vs Graduation Rate Assignment Example Calculating the Regression Line Compute the product of x and y deviations x 1 3 4 5 8 9 11 15 y 8 12 9 14 16 20 17 24 x x 6 4 3 2 1 2 4 8 y y 7 3 6 1 1 5 2 9 x x 2 36 16 9 4 1 4 16 64 y y 2 49 9 36 1 1 25 4 81 x x y y 42 12 18 2 …
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