Introduction to Regression line
- 1. Regression Line (with an example) Explained By Amarnath R https://sites.google.com/view/amarnath-r/
- 2. Example Consider a map Cities in the map The criteria is that the track must be straight-enough, That is, not curvy. Pave a railway track that connects every city Regression Line
- 3. How to draw the regression Line? x- axis y-axis Every city is called as sample in PR Every Sample should be represented by attributes / features In this case, every sample is represented by two features namely, x and y coordinates
- 4. Example x- axis y-axis Samples/ Cities X feature Y feature 1 6 6 2 10 12 3 14 3 4 22 9 5 24 25 6 32 17 7 33 30 8 43 40 9 47 22 10 52 35
- 5. Line Equation y = mx + b Assume m = 1 and b = 0 If x = 1, then y = 1(1) + 0 y = 1 If x = 2, then y = 2 If x = 3, then y = 3 If x = 4, then y = 4 If x = 5, then y = 5 If x = 6, then y = 6 If x = 7, then y = 7 If x = 8, then y = 8 If x = 9, then y = 9 If x = 10, then y = 10 m is slope and b is offset X Y 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10
- 6. Line Equation y = mx + b X Y 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 Assume m = 1 and b = 1 X Y 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 14 Assume m = 0 and b = 1 X Y 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 Assume m = 1 and b = 0 Assume m = 0 and b = 0 X Y 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0
- 7. Compute Line Equation for the samples Samples / Cities X feature Y feature 1 6 6 2 10 12 3 14 3 4 22 9 5 24 25 6 32 17 7 33 30 8 43 40 9 47 22 10 52 35 xmean : mean of x features ymean : mean of y features xymean : mean of x*y features xmeansqr : xmean * xmean xsqrmean : mean of x*x features m = Slope? and b = offset? m= 𝑥𝑚𝑒𝑎𝑛 ∗𝑦𝑚𝑒𝑎𝑛 −𝑥𝑦𝑚𝑒𝑎𝑛 𝑥𝑚𝑒𝑎𝑛𝑠𝑞𝑟 −𝑥𝑠𝑞𝑟𝑚𝑒𝑎𝑛 X.Y 36 120 42 198 600 544 990 1720 1034 1820 X.X 36 100 196 484 576 1024 1089 1849 2209 2704 28.3 19.9 710.4 1026.7 Compute m m= 28.3 ∗19.9 −710.4 800.89 −1026.7 xmeansqr = 800.89 m = .652 Compute b b = ymean – m * xmean b = 19.9–.652 * 28.3 b = 1.448 y = mx + b
- 8. Samples / Cities X feature Y feature 1 6 6 2 10 12 3 14 3 4 22 9 5 24 25 6 32 17 7 33 30 8 43 40 9 47 22 10 52 35 X.Y 36 120 42 198 600 544 990 1720 1034 1820 X.X 36 100 196 484 576 1024 1089 1849 2209 2704 28.3 19.9 710.4 1026.7 m = .652 b = 1.448 y = mx + b y = .652 * x + 1.448 Samples/ Cities X feature New Y 1 6 5.360214 2 10 7.968248 3 14 10.57628 4 22 15.79235 5 24 17.09636 6 32 22.31243 7 33 22.96444 8 43 29.48452 9 47 32.09256 10 52 35.3526
- 9. Research There is a VIP in this City Connecting 2 or more cities and ignoring the other cities
- 10. Thank you, If you have any queries Contact: https://sites.google.com/view/amarnath-r/