The determination of regression relationships using stepwise regression techniques
Stepwise regression routines are rapidly becoming a standard leature of large-scale computer statistical packages. They provide, in particular, a certain degree 01 flexibility in the selection of 'optimum' regression equations when one has available a large set of potential regressor varia...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
1973
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| Online Access: | https://eprints.nottingham.ac.uk/14053/ |
| _version_ | 1848791869982507008 |
|---|---|
| author | Payne, D. John |
| author_facet | Payne, D. John |
| author_sort | Payne, D. John |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Stepwise regression routines are rapidly becoming a standard leature of large-scale computer statistical packages. They provide, in particular, a certain degree 01 flexibility in the selection of 'optimum' regression equations when one has available a large set of potential regressor variables.
A major problem in the use of such routines is the determination of appropriate 'cut-off' criteria for terminating the procedures. There is a tendency in practice for standard F or t-statistics to be calculated at each step 01 the procedure, and for this value to be compared with conventional critical values.
In this thesis an attempt has been made to provide a more satisfactory rationale for (single-step) stepwise procedures. The approach taken is to assume that a 'true' model exists (the regressors in which are a subset of those available) and to investigate the distribution of statistics which, at each stage, seem relevant to the termination decision. This leads to the consideration of alternative tests at each step to those usually employed.
In the presence of considerable analytical complexity a simulation approach is used to obtain a comparison of the relative performances of various procedures. This study encompasses the use of forward, backward and mixed forward/backward procedures in both orthogonal and non-orthogonal set-ups. Procedures are evaluated both in terms of the 'closeness' of the finally selected model to the true one, and also in terms of prediction mean square-error.
The study ends with an investigation into the usefulness of stepwise regression in identifying and estimating stochastic regression relationships of the type encountered in the analysis of time series. |
| first_indexed | 2025-11-14T18:35:22Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-14053 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:35:22Z |
| publishDate | 1973 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-140532025-02-28T11:28:35Z https://eprints.nottingham.ac.uk/14053/ The determination of regression relationships using stepwise regression techniques Payne, D. John Stepwise regression routines are rapidly becoming a standard leature of large-scale computer statistical packages. They provide, in particular, a certain degree 01 flexibility in the selection of 'optimum' regression equations when one has available a large set of potential regressor variables. A major problem in the use of such routines is the determination of appropriate 'cut-off' criteria for terminating the procedures. There is a tendency in practice for standard F or t-statistics to be calculated at each step 01 the procedure, and for this value to be compared with conventional critical values. In this thesis an attempt has been made to provide a more satisfactory rationale for (single-step) stepwise procedures. The approach taken is to assume that a 'true' model exists (the regressors in which are a subset of those available) and to investigate the distribution of statistics which, at each stage, seem relevant to the termination decision. This leads to the consideration of alternative tests at each step to those usually employed. In the presence of considerable analytical complexity a simulation approach is used to obtain a comparison of the relative performances of various procedures. This study encompasses the use of forward, backward and mixed forward/backward procedures in both orthogonal and non-orthogonal set-ups. Procedures are evaluated both in terms of the 'closeness' of the finally selected model to the true one, and also in terms of prediction mean square-error. The study ends with an investigation into the usefulness of stepwise regression in identifying and estimating stochastic regression relationships of the type encountered in the analysis of time series. 1973 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/14053/1/468476.pdf Payne, D. John (1973) The determination of regression relationships using stepwise regression techniques. PhD thesis, University of Nottingham. |
| spellingShingle | Payne, D. John The determination of regression relationships using stepwise regression techniques |
| title | The determination of regression relationships using stepwise regression techniques |
| title_full | The determination of regression relationships using stepwise regression techniques |
| title_fullStr | The determination of regression relationships using stepwise regression techniques |
| title_full_unstemmed | The determination of regression relationships using stepwise regression techniques |
| title_short | The determination of regression relationships using stepwise regression techniques |
| title_sort | determination of regression relationships using stepwise regression techniques |
| url | https://eprints.nottingham.ac.uk/14053/ |