Home / DOE / Analyze / Uncoded Coefficients
Uncoded Coefficients¶
This command fits the same model as Run Regression but reports the coefficients in the factors' own units instead of coded units. The coding instructions on the design sheet are ignored and the X matrix is built from the actual factor values.
QXL DOE New > Analyze Design > Uncoded Coefficients
When to use it¶
Use it at the end, once you have decided which terms belong in the model, when you want the equation in real units so it can be handed to someone else or used in a calculation.
For example, with Temperature running from 20 to 40 degrees, an ordinary regression replaces 20 with \(-1\) and 40 with \(+1\) before fitting, and its coefficient is the change in the response per coded unit. The uncoded version keeps 20 and 40, and its coefficient is the change per degree, which is the number a process engineer can use directly.
Why the p values are hidden by default¶
This is the important limitation, and it is why the report looks different from the coded one.
Coding removes most of the correlation between a term and the interactions and squares built from it. Without coding, a factor and its own square are strongly correlated, so the variance inflation factors climb, the standard errors inflate with them, and the p values that follow are not trustworthy. A term that is clearly significant in coded units can appear insignificant here purely because of that correlation.
So the 2-tail p values are hidden by default. The report says so in its heading block, in red, on the line under Regression in uncoded units:
P(2 Tail) values are not displayed by default when using uncoded coefficients. To change this option go to Settings, and select 'Display P Values' option.
The control that message names does not exist. The setting is the group box Show P-Value for the uncoded
regression, on the Regression page of DOE Options. The sheet's
'Display P Values' wording is stale and is recorded in code-flags-for-engineering.md.
Custom designs are exempt. On a custom design the p values are printed whatever the setting says, and no notice appears.
Uncoded Coefficients is an independent ribbon button. Nothing in the software requires it to be run before or after Run Regression.
What you get¶
A worksheet called Uncoded Regression, alongside the ordinary Regression sheet rather than replacing it, so both reports are available at once. Everything else about the sheet matches the coded report, described in Regression Results for OLS.
What changes and what does not¶
| Coded regression | Uncoded regression | |
|---|---|---|
| The fitted model | the same | the same |
| Predicted values | the same | the same |
| R squared, adjusted R squared, F | the same | the same |
| Coefficients | per coded unit, comparable between factors | per real unit, in each factor's own units |
| Variance inflation factors | low, coding removes most correlation | inflated |
| p values | reported | hidden by default, except on a custom design |
The two reports describe one model in two vocabularies. They predict identically; they disagree only about what a coefficient means.
How coding works¶
Every quantitative factor is put on a common scale before the regression runs. One expression does it, whichever coding is in force, using a centre \(m_c\) and a scale \(s_c\) that the coding chooses:
A categorical factor is never coded this way. Its coded value is \(1\), and the level it sits at selects which coefficient is used instead.
An interaction's coded value is the product of the coded values of the factors in it.
Uncoded leaves the factor values exactly as entered, so the coefficients come out in the factor's own units.
Full details: Design Coding.