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Stat 1301 The Regression Line

Stat 1301 The Regression Line. Recall: SD Line --. goes through point of averages passes through “heart” of elliptical shaped cloud. Selling price (Y). Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82. Age in years (X).

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Stat 1301 The Regression Line

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  1. Stat 1301The Regression Line

  2. Recall: SD Line -- • goes through point of averages • passes through “heart” of elliptical shaped cloud

  3. Selling price (Y) Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82 Age in years (X)

  4. Selling price (Y) Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82 SD Line Age in years (X)

  5. The Regression Line A “smoothed” graph of averages Used to predict Y (the dependent variable) from knowing X (the independent variable)

  6. The Regression Line(continued) Passes through the point of averages (AVGx, AVGy) r SDy Has slope m = SDx i.e. a change of 1SDx for independent variable is associated with r SDy change in dependent variable

  7. SD Line Regression Line

  8. Selling price (Y) Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82 Age in years (X)

  9. Selling price (Y) Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82 Regression Line Age in years (X)

  10. Selling price (Y) Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82 SD Line Age in years (X)

  11. Selling price (Y) Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82 Age in years (X)

  12. NOTE: The regression line has smaller slope than SD line • i.e regression line is not as steep

  13. Easier Way to Predict - Use Regression Line(Chapter 12) Equation: y = mx + b m = slope b = y-intercept where rSDy m = SDxb = AVGy - mAVGx

  14. Predicting Y whenyou know X Put value for X into regression equation and solve for Y

  15. What height would you predict for a son whose father is: (a) 72” tall (b) 64” tall (c) 68” tall

  16. Selling price (Y) Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290 SDy = 6,044 (Price) r = - 0.82 Regression Line Age in years (X)

  17. Used Car Data Price AVG = 11,290 SD = 6044 Age AVG = 6 yrs SD = 3 yrs r = -.82 1. Find the equation of the regression line for predicting Price from Age 2. Predict Price if car is (a) 3 years old (b) 10 years old

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