Linear regression model

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Rupam Fedujwar

Linear regression model.

Engineering

Hey where are
You going?
Man for shopping.

Zone Trip Generation Student Enrollment
01 560 150
02 340 196
03 860 553
04 480 219
05 280 96
06 560 256
07 120 100

How much data required to
generate good relationship?

First draw a line through the data.
Student Enrollment
TripGeneration

Measure the distance from
the line to data, square
each distance, and then add
them up.
The distance from a
line to a data point is
called a “residual”.
Student Enrollment
TripGeneration

Draw any new line,
measure the residual,
square them , and then
sum up the square.
Student Enrollment
TripGeneration

Rotate the line little bit more…..
Student Enrollment
TripGeneration

Sum up the squared
residuals..
Student Enrollment
TripGeneration

Sum of square
residuals
Different Rotation
After the bunch of rotations,
you plot the sum of squared
residual and corresponding
rotation.

Sum of square
residuals
After the bunch of rotations,
you plot the sum of squared
residual and corresponding
rotation.

Sum of square
residuals
Find the rotation that has
the least sum of square

Sum of square
residuals
This rotation is one with
the “least squares”, it be
the best fit for data.

This is our “least squares”
rotation line
Student Enrollment
TripGeneration

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Linear regression model

1. Mr. Rupam R. Fedujwar Transportation Engineering School of Infrastructure IIT Bhubaneswar

4. Hey where are You going? Man for shopping.

5. Zone Trip Generation Student Enrollment 01 560 150 02 340 196 03 860 553 04 480 219 05 280 96 06 560 256 07 120 100

9. How much data required to generate good relationship?

10.

11. TripGeneration Student Enrollment

12. Student Enrollment TripGeneration

13. Student Enrollment TripGeneration

14.

15. Student Enrollment TripGeneration

16. First draw a line through the data. Student Enrollment TripGeneration

17. Measure the distance from the line to data, square each distance, and then add them up. The distance from a line to a data point is called a “residual”. Student Enrollment TripGeneration

18. Draw any new line, measure the residual, square them , and then sum up the square. Student Enrollment TripGeneration

19. Rotate the line little bit more….. Student Enrollment TripGeneration

20. Sum up the squared residuals.. Student Enrollment TripGeneration

21. Sum of square residuals Different Rotation After the bunch of rotations, you plot the sum of squared residual and corresponding rotation.

22. Sum of square residuals After the bunch of rotations, you plot the sum of squared residual and corresponding rotation.

23. Sum of square residuals

24. Sum of square residuals

25. Sum of square residuals

26. Sum of square residuals Find the rotation that has the least sum of square

27. Sum of square residuals This rotation is one with the “least squares”, it be the best fit for data.

28. This is our “least squares” rotation line Student Enrollment TripGeneration

Linear regression model

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