XTXIXTY page at the PumaGP website

This text is made to describe the use of the XTXIXTY section at the PumaGP team website:
http://pumagp.0fees.net/index.php?do=xtxixty_p
and the additional "Chosen formulas" page:
http://pumagp.0fees.net/index.php?do=chosen_formulas

Action 1) Data are gathered into local Table editor and arranged in the way X1, X2 ... Xn Y. 

For example, if we need to find the formula for the fuel sonsumption, we build table which has next columns:
 - "Fuel consumption" track parameter;
 - Engine level;
 - Electronics level;
 - Driver Experience;
 - Driver Technical Insight;
 - Fuel consumption, L/km (this one will be Y, so we put it at the right end of table)

Action 2) PumaGP website, XTXIXTY page. There we click "New project"  link, set the name of this new project and make it public (for the community of the website. Access denied for unregistered ).

Or just select existing project in the dropdown list (available options are public projects and projects created by the user who is watching this page).

Action 3) The data table contains string values ("Very low", "Low"...) They should be converted to the numbers. In order to do this automatically at the data upload (action 5) the replacement rules should be written. 

 - we click at "Replacement rules" link;

 - in the input field each row corresponds to one pair of values "Text to be replaced - number which will take place". Separator between them is Tab symdol.

 Notes: 

 - Text is case-sensitive.

 - Each string should not be the substring to the text value which comes later in the list (For example, "high" can be placed only after "very high", NOT before. But due to case-sensitiveness "High" is not the substring to "Very high", and in this case the order is not important).

 In the given example we should write next:

Very low 1
Low 2
Medium 3
High 4
Very high 5

Action 4) Description of the project can be written in the Description section under the Replacement rules.

Action 5) Data from the Action 1 are inputted in the Data section under "Description".

 - Decimal separator should be "." (point, not comma).

Action 6) We select "New" in the "Formula in project" dropdown list. (Or one of the formulas, created earlier by own hands, if we want to rewrite it).

Then we 

 a) copy some datarows from the Project Data into the Formula Data field

or

 b) check the "Random rows from project" checkbox and input the number of rows to select. Rules of autoselection: each pair of rows should have at least one pair of values which are different by at least 1.

Example: 

3 6 7 103 51 0.693 — will be taken

3 6 7 103 51 0.693 — will be ignored because X values are the same as in previous

4 5 8 117 60 0.705 — will be taken

3 6 7 103 52 0.693 — will be taken because one of X values is different by 1 comparing to the first row.

Then we select which columns should be used in the formula: X0 (free number), X1...Xn (columns from the data table), Xi^2 (squared values from the data table), Xi*Xj (product of each pair of columns from the data table).

Action 7) We click the Calculate button and see th result.

First Table contains calculated Y values for the data used in formula calculation.

Second Table contains maximal and minimal difference in percentage of real Y: (Ycalc – Yreal)/Yreal * 100%, and also the variance or Ycalc–Yreal (looks like there is mistake in its calculation).

Difference Max	Difference Min	Variance
1.037%	-0.759%	0

Third Table contains calculated Y values for all data of the project.

Action 8) If formula looks good and differences Ycalc–Yreal are all low, we can check this formula as the chosen one. For this we click the "Add this function to the chosen ones (or delete from)" link which is under the result tables, and then (if the text near says "Is NOT chosen") — the button in this section.

Next click at this button will remove the "chosen" mark. Another click will add it again and so on.

Action 9) "Chosen formulas" page. There we select project, formula in project. (Description, replacement rules and "Data example" are shown under "Project info" link), then we input new X matrix in Data field.

For example, the text from "Data example" can be pasted there:

We click "Calculate" button and recieve the result (X1^2 from one of the previous screens was clicked back):

1	X1	X2	X3	X4	X5	X12	X22	X32	X42	X52	X1 X2	X1 X3	X1 X4	X1 X5	X2 X3	X2 X4	X2 X5	X3 X4	X3 X5	X4 X5	Y calc
1	3	4	5	59	123	9	16	25	3481	15129	12	15	177	369	20	236	492	295	615	7257	0.722

So, due to this formula, if we have track with Medium fuel consumption (X1 = 3),  Engine 4, Electronics 5, Driver Experience 59 and Driver TI 123, the fuel cosumption should be 0.722 L/km.