The phrase "auxiliary regression" is correct and usable in written English.
It can be used in statistical contexts, particularly when discussing methods that involve regression analysis as a supplementary tool.
Example: "In our analysis, we employed auxiliary regression to better understand the relationship between the variables."
Alternatives: "supplementary regression" or "secondary regression".
The predicted values from this auxiliary regression are used to transform equation (5).
Further, a standard Park test, i.e., an auxiliary regression of the form exp ( ∊ i ) ^ = ρ X indicated that none of the explanatory variables are statistically significant predictors of log-scale residuals.
In this equation, ( {widehat{Z;}}_i ) is the linear projection of SP i on X i and Z i, i.e., the fitted values for SP obtained from auxiliary regression (7): {mathrm{SP}}_i={X}_idelta +{Z}_imu +{nu}_i (7).
I derive the consistency of OLS estimator (widehat {rho _{1}}) in Eq. (7), where the dependent variable has a measurement error due to using the proxy and the independent variable is generated from an auxiliary regression.
In order to check for endogeneity between the variables used, we use the version of the Hausman test (Hausman 1978) proposed by Davidson and MacKinnon (1989, 1993), which tests for exogeneity by running an auxiliary regression.
It is possible to run an auxiliary regression of the heteroskedastic variance as a function of one or more of the explanatory variables, i.e., ф ^ = exp ( ∊ i ) ^ = ρ X ; where ρ is a vector of regression coefficients.
All time varying variables were averaged over the whole panel period and used in the auxiliary regressions for the Wooldridge-type estimators for determining their effect on the individual specific term.
Since multilateral resistance to migration generates an upward bias on the impact of the origin country unemployment to inflows, estimates decreased slightly under the specification with auxiliary regressions, where the decrease of inflows associated to an increase of 10 pp in the unemployment rate is only of 0.1 pp.
This test performs auxiliary regressions that add in powers of the fitted values to the original equations.
69 In the auxiliary regressions, the averaged value of a GP visit during the past 12 months variable was correlated in five of the six health check-ups with the individual-specific term for time-invariant unobserved heterogeneity and could also be caused by unobserved time-invariant factors that have an influence on probability of a GP visit and uptake of the different health check-ups.
Generally, this auxiliary-regression approach is thought to be cumbersome and there is no simple fix if the form of heteroskedasticity is unknown.
