Best Basis

Usage notes

In this exercise we consider the following best basis problem:

, where

is a given

matrix.
We are looking for the choice of two columns of

that give the most significant contribution to the solution of eq.

Throughout the exercise you will need to calculate the residuum

for a given column set of the matrix

. For this purpose you have the following tool:

column set ___________________ e.g. 2,4,5

Residuum r = Write the column set and after pressing the Calculate button you get the residuum.

a) Stepwise Regression

For this particular problem is it better to use stepwise regression or backward stepwise regression?

stepwise regression

backward stepwise regression

Perform stepwise regression.
Which column does reduce the error the most?
___________________

Which column do you add to complete the solution?
___________________

b)

Now try performing backward stepwise regression. Which is the first column to be removed?
___________________

Which is the second column to be removed?
___________________

Which is the last column to be removed?
___________________

Observe: 1,4 is a bad result. Compare the residuum for 1,4 with the residuum in part a).

c) Steepest Descent

Start from the pair 1 2 (residuum = 85.50). Which is the best neighbour?
___________________ with residuum ___________________ (rounded to 4 digits)

Can we continue with another step?

Yes

No

d) Early Abort

Now use the early abort algorithm starting from the column pair 1 5. Instead of using a random choice of neighbour use the following order:

1 2	1 3	1 4	1 5	2 3	2 4	2 5	3 4	3 5	4 5

Which is the next step?
___________________

Can we continue with another step?

Yes

No

Observation: The data used in this exercise are built artificially to show you some problematic aspect of the different algorithms.

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