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Multiple Linear Regression Analysis THE OPTION SPECIFICATION It is possible to have the program perform some tasks optionally by providing an option specification in a job. It consists of the keyword "Options" followed by a list of option names or corresponding option numbers (the option statement), separated by commas and terminated with a ';' (semicolon). The following ten options are available: option number option name 1 Transformed data matrix 2 Correlation matrix 3 Residual analysis 4 No regression analysis 5 Process submodels 6 Print input data 7 No input data rewind 8 Save original model 9 Test reduced model 10 Missing values Options 1, 2, 3 and 6 cause the corresponding piece of information to be printed. However, option 1 lists only those (possibly transformed) variables that are present in the model formula in a neat tabular form, while option 6 lists all the original input data serially (eleven numbers per line) without any special layout, because the input data consists (by definition) of an unstructured series of numbers (cf. "Help"/Data). Option 4 suppresses the regression analysis; it is meant to be used in combination with option 1 and/or 2. Option 5 causes the program to process submodels, which are formed by a form of backward elimination: each time the last term from the right hand part from the model formula is omitted, by deleting the last column from the design matrix, and a regression analysis is performed with the reduced design matrix. Messages are generated about which terms are omitted, while further processing of the job ceases when the resulting model formula is of the form: y = c. Moreover a test is made (under the usual assumptions) whether the omitted terms did contribute significantly to the regression sum of squares (cf. "Help"/Tests). To option 5 a specifier list can be appended, to prevent the pro- duction of waste output for unwanted submodels. In this list the number of terms to be omitted from the model formula (counting backwards, starting at the end) must be given enclosed in parentheses. For example the option: Process submodels (6, 10) instructs the program to process only two submodels, one with the last six terms omitted and one with the last ten terms omitted (from the original model formula). If the user asks for more terms to be omitted than are present in the model formula, an error message is supplied and the execution of that job is terminated. Moreover, if no explicit specifier list is appended to option 5, the options 2 and 3 yield no effect (even if specified), which is also to prevent the production of waste output for the submodels. Option 7 gives the user the opportunity to process consecutive pieces of input data in consecutive jobs. Normally the processing of the input data for each job starts with the first number in the data specification (or with the first number in the datastream), and the program gives a (warning) message if the input formula does not match the input data precisely. This option disengages the message and causes the program to continue processing input data where the previous job had finished. Option 8 causes the residual degrees of freedom and residual sum of squares from the current job to be saved, in order to be able in the next job, by means of specifying option 9, to test whether the model under consideration in that next job, shows a significant increase in residual sum of squares in comparison with the model in the previous job. In effect this gives the possibility of testing a hypothesis concerning a linear combination of the parameters from a model (cf. "Help"/Tests), for instance: "Model 1" y = b1 * x1 + b2 * x2 + b3 * x3; "Options" Save original model; "Run" "Model 2" y - 4 * x1 = b2 * (x1 + x2) + b3 * x3; "Options" Test reduced model; "Run" causes the null hypothesis: b1 = b2 + 4 to be tested (in the second job). Option 10 may be used to identify some observations or repetitions as 'missing'. In a specifier list, appended to this option, the missing values must be given enclosed in parentheses. When a repetition equal to a missing value is encoutered in the input data, the corresponding set of repetitions for the dependent variable(s) is not included in the design matrix. When an observation equal to a missing value is encountered in the input data, or when none of the repetitions are included in the design matrix, the corresponding set of observations for the independent variables together with the (possibly empty) set of repetitions for the dependent variable(s) (i.e. the 'case') is not included in the design matrix.