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Linear regression
- 10. EXAMPLE • Example of simple linear regression which has one independent variable.
- 15. Least Squares Estimationof b0, b1 • b0 Mean response when x=0 (y-intercept) • b1 Change in mean response when x increases by 1 unit (slope) • b0, b1 are unknown parameters (like m) • b0+b1x Mean response when explanatory variable takes on the value x • Goal: Choose values (estimates) that minimize the sum of squared errors (SSE) of observed values to the straight-line: 2 n 2 ^ ^ ^ ^ ^ ^ y b 0 b1 x SSE i 1 yi y i i 1 yi b 0 b 1 xi n
- 16. The least squaresestimate of the slope coefficient β1 of true regression line is β1= Σ(Xi-X’)(Yi-Y’) Σ (Xi-X’)2 The least squares estimate of the intercept β0 of true regression line is β0 = Y’ – β1x’
- 19. X Y Temperature Sales 63 1.52 70 1.68 73 1.8 75 2.05 80 2.36 82 2.25 85 2.68 88 2.9 90 3.14 91 3.06 92 3.24 75 1.92 98 3.4 100 3.28 92 3.17 87 2.83 84 2.58 88 2.86 80 2.26 82 2.14 76 1.98
- 20. Ice Cream Sales 4 3.5 3 2.5 2 1.5 1 0.5 0 0 20 40 60 80 100 120
- 22.