{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/64522"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/64522","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A short cut method for linear regression","abstract":"This thesis reviews and discusses the so-called “Group Averages method\" in the linear regression, the quadratic regression, and the functional relation situations. In the linear and quadratic regression situations, under the assumption of X<sub>i</sub> equally spaced, the efficiency of the Group Averages estimator is quite satisfactory as compared with Least Squares estimators. In the functional relation situation we used the Group Averages method and the Maximum Likelihood method for estimation of parameters. To compare their efficiencies we used the variance of the Group Averages estimator which was given by Dorff and Gurland [3], and developed the variance of Maximum Likelihood estimators. Under the assumption of X<sub>i</sub> equally spaced, we round the efficiency of the Group Averages estimator to be quite satisfactory. However, caution is needed for using the Group Averages method in functional relationships, since it requires the following condition to be satisfied: Pr {|d<sub>i</sub>| ≥ ½ c} negligible Where c = Min. |X<sub>i+1</sub> - X<sub>i</sub>|.","abstract_html":"This thesis reviews and discusses the so-called “Group Averages method&quot; in the linear regression, the quadratic regression, and the functional relation situations. In the linear and quadratic regression situations, under the assumption of X&lt;sub&gt;i&lt;/sub&gt; equally spaced, the efficiency of the Group Averages estimator is quite satisfactory as compared with Least Squares estimators. In the functional relation situation we used the Group Averages method and the Maximum Likelihood method for estimation of parameters. To compare their efficiencies we used the variance of the Group Averages estimator which was given by Dorff and Gurland [3], and developed the variance of Maximum Likelihood estimators. Under the assumption of X&lt;sub&gt;i&lt;/sub&gt; equally spaced, we round the efficiency of the Group Averages estimator to be quite satisfactory. However, caution is needed for using the Group Averages method in functional relationships, since it requires the following condition to be satisfied: Pr {|d&lt;sub&gt;i&lt;/sub&gt;| ≥ ½ c} negligible Where c = Min. |X&lt;sub&gt;i+1&lt;/sub&gt; - X&lt;sub&gt;i&lt;/sub&gt;|.","abstract_has_math":false,"creators":["Perng, Shian-koong"],"institution":"Virginia Polytechnic Institute","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Statistics","degree_department":"Statistics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1961,"date_issued":"1961","date_published":"1961","updated_at":"2026-07-22T22:20:18Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/64522","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Statistics"]},{"key":"dc:creator","label":"Author","values":["Perng, Shian-koong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-02-01T14:44:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-01T14:44:38Z"]},{"key":"dc:date.issued","label":"Date","values":["1961"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/64522"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis reviews and discusses the so-called “Group Averages method\" in the linear regression, the quadratic regression, and the functional relation situations. In the linear and quadratic regression situations, under the assumption of X<sub>i</sub> equally spaced, the efficiency of the Group Averages estimator is quite satisfactory as compared with Least Squares estimators. In the functional relation situation we used the Group Averages method and the Maximum Likelihood method for estimation of parameters. To compare their efficiencies we used the variance of the Group Averages estimator which was given by Dorff and Gurland [3], and developed the variance of Maximum Likelihood estimators. Under the assumption of X<sub>i</sub> equally spaced, we round the efficiency of the Group Averages estimator to be quite satisfactory. However, caution is needed for using the Group Averages method in functional relationships, since it requires the following condition to be satisfied: Pr {|d<sub>i</sub>| ≥ ½ c} negligible Where c = Min. |X<sub>i+1</sub> - X<sub>i</sub>|."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A short cut method for linear regression"]}]}],"canonical_facts":{"dc:contributor.department":["Statistics"],"dc:creator":["Perng, Shian-koong"],"dc:date.accessioned":["2016-02-01T14:44:38Z"],"dc:date.available":["2016-02-01T14:44:38Z"],"dc:date.issued":["1961"],"dc:description.abstract":["This thesis reviews and discusses the so-called “Group Averages method\" in the linear regression, the quadratic regression, and the functional relation situations. In the linear and quadratic regression situations, under the assumption of X<sub>i</sub> equally spaced, the efficiency of the Group Averages estimator is quite satisfactory as compared with Least Squares estimators. In the functional relation situation we used the Group Averages method and the Maximum Likelihood method for estimation of parameters. To compare their efficiencies we used the variance of the Group Averages estimator which was given by Dorff and Gurland [3], and developed the variance of Maximum Likelihood estimators. Under the assumption of X<sub>i</sub> equally spaced, we round the efficiency of the Group Averages estimator to be quite satisfactory. However, caution is needed for using the Group Averages method in functional relationships, since it requires the following condition to be satisfied: Pr {|d<sub>i</sub>| ≥ ½ c} negligible Where c = Min. |X<sub>i+1</sub> - X<sub>i</sub>|."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/64522"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["A short cut method for linear regression"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-22T22:20:18Z"}