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Regression diagnostic
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<h2 id="introduction">Introduction</h2> <p>Regression diagnostics have often been developed or were initially proposed in the context of <a href="/facts/Linear_regression/5n998IhK">linear regression</a> or, more particularly, <a href="/facts/Ordinary_least_squares/q7H9k5vM">ordinary least squares</a>. This means that many formally defined diagnostics are only available for these contexts. </p> <h2 id="assessing-assumptions">Assessing assumptions</h2> Distribution of model errors <ul><li><a href="/facts/Normal_probability_plot/Wv4jeKzQ">Normal probability plot</a></li></ul> <a href="/facts/Homoscedasticity/50v2qyEN">Homoscedasticity</a> <ul><li><a href="/facts/Goldfeld%25E2%2580%2593Quandt_test/zFH3kxVl">Goldfeld–Quandt test</a></li> <li><a href="/facts/Breusch%25E2%2580%2593Pagan_test/2CcU4AQM">Breusch–Pagan test</a></li> <li><a href="/facts/Park_test/zWYaUFdo">Park test</a></li> <li><a href="/facts/White_test/TSAbaq7e">White test</a></li></ul> Correlation of model errors <ul><li><a href="/facts/Breusch%25E2%2580%2593Godfrey_test/1epmUIYX">Breusch–Godfrey test</a></li></ul> <h2 id="assessing-model-structure">Assessing model structure</h2> Adequacy of existing explanatory variables <ul><li><a href="/facts/Partial_residual_plot/LVApnTEP">Partial residual plot</a></li> <li><a href="/facts/Ramsey_RESET_test/2Rvgf3LW">Ramsey RESET test</a></li> <li><a href="/facts/F_test/Kq8lzNqY">F test</a> for use when there are replicated observations, so that a comparison can be made between the <a href="/facts/Lack-of-fit_sum_of_squares/xpo4Jqjn">lack-of-fit sum of squares</a> and the pure error sum of squares, under the assumption that model errors are <a href="/facts/Homoscedastic/50v2qyEN">homoscedastic</a> and have a <a href="/facts/Normal_distribution/UapjjPyQ">normal distribution</a>.</li></ul> Adding or dropping explanatory variables <ul><li><a href="/facts/Partial_regression_plot/gkfeBBlz">Partial regression plot</a></li> <li><a href="/facts/Student%2527s_t_test/dMH8uC28">Student's t test</a> for testing inclusion of a single explanatory variable, or the <a href="/facts/F_test/Kq8lzNqY">F test</a> for testing inclusion of a group of variables, both under the assumption that model errors are <a href="/facts/Homoscedastic/50v2qyEN">homoscedastic</a> and have a <a href="/facts/Normal_distribution/UapjjPyQ">normal distribution</a>.</li></ul> Change of model structure between groups of observations <ul><li><a href="/facts/Structural_break_test/F9ubwktl">Structural break test</a> <ul><li><a href="/facts/Chow_test/QYGUdETS">Chow test</a></li></ul></li></ul> Comparing model structures <ul><li><a href="/facts/PRESS_statistic/u0ksCavz">PRESS statistic</a></li></ul> <h2 id="important-groups-of-observations">Important groups of observations</h2> Outliers Influential observations <ul><li><a href="/facts/Leverage_(statistics)/5lkfBFWo">Leverage (statistics)</a>, <a href="/facts/Partial_leverage/nbH29aB9">partial leverage</a></li> <li><a href="/facts/DFFITS/nDSwwkcR">DFFITS</a></li> <li><a href="/facts/Cook%2527s_distance/Lofo52jQ">Cook's distance</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Everitt, B.S. (2002) The Cambridge Dictionary of Statistics, CUP. ISBN 0-521-81099-X (entry for Regression diagnostics) <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>