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80 6 Regression15 RDISPLAY [PRINT=accumulated; FPROBABILITY=yes]Regression analysisAccumulated analysis of varianceChange d.f. s.s. m.s. v.r. F pr.+ Windsp 1 1.4952 1.4952 10.44 0.002+ Rain 1 0.3933 0.3933 2.75 0.100+ Windsp.Rain 1 0.0323 0.0323 0.23 0.636Residual 108 15.4677 0.1432Total 111 17.3884 0.1567Here a Common line (in fact, a simple linear regression) would be enough. However, wewill refit the parallel lines to illustrate how to get a parameter for each intercept, ratherthan parameters for differences from the reference level.16 TERMS [FULL=yes] Windsp + Rain + Windsp.Rain17 FIT [CONSTANT=omit; FPROBABILITY=yes; TPROBABILITY=yes] \18 Windsp + RainRegression analysisResponse variate: LogsulphurFitted terms: Windsp + RainSummary of analysisSource d.f. s.s. m.s. v.r. F pr.Regression 2 1.89 0.9442 6.64 0.002Residual 109 15.50 0.1422Total 111 17.39 0.1567Change -1 -0.39 0.3933 2.77 0.099Percentage variance accounted for 9.2Standard error of observations is estimated to be 0.377.Message: the following units have high leverage.Unit Response Leverage30 0.477 0.10272 0.699 0.073Estimates of parametersParameter estimate s.e. t(109) t pr.Windsp -0.02193 0.00818 -2.68 0.008Rain no 1.1235 0.0891 12.62
6.6 Practical 81regression coefficient for each level of Rain by also omitting Windsp i.e.FIT [CONSTANT=omit; FPROBABILITY=yes; TPROBABILITY=yes]\Rain + Windsp.Rain6.6 PracticalSpreadsheet file Calcium.gsh (in the Data folder) contains a data set, discussed inSections 4.6 and 6.4 of McConway, Jones & Taylor (1999, Statistical Modelling usingGENSTAT, Arnold, London), which contains information about mortality in 61 towns.The aim is to study how this relates to the calcium concentration in the drinking watersupply.Fit a linear regression of mortality on calcium. Are the assumptions satisfied better bytransforming mortality to logarithms?Perform a simple linear regression with groups to see how the relationship is affectedby region.6.7 Other regression facilitiesIn addition to the linear regression models, described in this chapter, GenStat coversmany other types of regression model, including smoothing splines and locally weightedregression. It also has commands and menus for other regression analyses including• all-subsets regression,• screening tests,• polynomial regression,• nonlinear curves (both standard and user-defined),• split-line regression,• generalized linear models (for non-Normal data like counts and proportions),• ordinal regression,• generalized additive models,• generalized linear mixed models,• hierarchical generalized linear models,• regression trees and• quantile regression.Menus for some of these are described in the Guide to Regression, Nonlinear andGeneralized Linear Models in GenStat. All the main commands are described, withexamples, in the Guide to the GenStat Command Language, Part 2 Statistics, Chapter3. (These Guides can both be accessed from within GenStat for Windows by selectingsub-options of the GenStat Guides option of the Help menu on the menu bar.)The other regression commands are in the GenStat Reference Manual, Part 3Procedure Library PL23 (to open, select the Procedure Library sub-option of the GenStatReference Manual option of the Help menu on the menu bar).
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