Calculating the Non-Linear Regression Method

Below is the example of using the GetMs operation to calculate an equation. The request contains an instance of opened modeling container, equation calculation pattern, and parameters of operation execution. The response contains an instance of the model that contains an equation with calculation results.

To execute the example the equation must be calculated using the Non-Linear Regression method.

SOAP request:

<s:Envelope xmlns:s="http://schemas.xmlsoap.org/soap/envelope/">

<s:Body xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">

<id>CGNGLNJJAFNBFOAEAMLDKJBMDFDMIKBECLCCPAGGMMNHDHAO!M!S!CCFELIOJJAFNBFOAEGCJLMLPJNCHIHJEEHKPLONIGDEKIBJDL</id>

</tMs>

<obInst>false</obInst>

<all>false</all>

<item>

</method>

</formulas>

</equationsFormula>

</transformSlice>

</transformVariable>

</transform>

</modelPattern>

</entryKeys>

</calcChainPattern>

</metamodel>

</problem>

</item>

</pattern>

</modelKeys>

</execParams>

</tArg>

</GetMs>

</s:Body>

</s:Envelope>

SOAP response:

<soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/">

<soapenv:Body>

<id>CGNGLNJJAFNBFOAEAMLDKJBMDFDMIKBECLCCPAGGMMNHDHAO!M!S!CCFELIOJJAFNBFOAEGCJLMLPJNCHIHJEEHKPLONIGDEKIBJDL</id>

</id>

<item>

<id>MODEL_NEW</id>

<n>MODEL_NEW</n>

<type>Problem</type>

<its>

<Item>

<n>MyOutputVavable|A[t] = MyInputVavable|A[t] * a + b, 1990A1-2010A1</n>

<type>Model</type>

<model>

<its>

<Item>

<id>VARIABLES_89670</id>

<n>Variables</n>

<its>

<Item>

<id>MyOutputVavable|A</id>

<n>MyOutputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</Item>

</its>

</slices>

<attributeType>Series</attributeType>

</Item>

</its>

</outputs>

<its>

<it>

<kind>NonLinearRegression</kind>

<method>LinTrend</method>

</specifiedTerm>

</missingData>

</initialApproximation>

<slice>

<id>MyOutputVavable|A</id>

<n>MyOutputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</slice>

<lag />

<termToText>{MyOutputVavable|A[t]}</termToText>

<lag>PrecidingValue</lag>

<dependence>Linear</dependence>

</inversion>

<slice>

<id>MyOutputVavable|A</id>

<n>MyOutputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</slice>

</termInfo>

</unitInfo>

</result>

<its>

<Item>

<slice>

<id>MyInputVavable|A</id>

<n>MyInputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</slice>

<termToText>{TS(MyInputVavable|A[t+1], Linear)}</termToText>

<lag>PrecidingValue</lag>

<dependence>Linear</dependence>

</inversion>

<slice>

<id>MyInputVavable|A</id>

<n>MyInputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</slice>

</termInfo>

</unitInfo>

</Item>

<Item>

<slice>

<id>MyInputVavable|A</id>

<n>MyInputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</slice>

<termToText>{MyInputVavable|A[t]}</termToText>

<lag>PrecidingValue</lag>

<dependence>Linear</dependence>

</inversion>

<slice>

<id>MyInputVavable|A</id>

<n>MyInputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</slice>

</termInfo>

</unitInfo>

</Item>

</its>

</operands>

</coefficients>

<its>

<Item>

</Item>

<Item>

</Item>

</its>

</statCoefficients>

<optimizationMethod>LevenbergMarquardt</optimizationMethod>

</nonLinearRegression>

<input>

<lag>PrecidingValue</lag>

<dependence>Linear</dependence>

</inversion>

<slice>

<id>MyOutputVavable|A</id>

<n>MyOutputVavable|A</n>

<its>

<Item>

<id>

</id>

</Item>

</its>

</selections>

<its>

<Item>

</Item>

</its>

</parametrizedDimensions>

</unitInfo>

</slice>

</input>

</addFactor>

</series>

<its>

<Item>

<fact>

</fact>

</modelling>

</residuals>

<input>

</input>

<its>

<it>

<termToText>{MyInputVavable|A[t]}</termToText>

<serie>

</serie>

<lag>PrecidingValue</lag>

<dependence>Linear</dependence>

</inversion>

</it>

</its>

</factors>

</Item>

</its>

<dates>

</dates>

</evaluateSeries>

<lag>PrecidingValue</lag>

<dependence>Linear</dependence>

</inversionInfo>

</method>

</it>

</its>

</formulas>

<its />

</series>

<kind>Simple</kind>

<displayTermsAs>Derive</displayTermsAs>

</displaySettings>

<calculationType>Serie</calculationType>

<calculationDirection>Forward</calculationDirection>

</transform>

<calculationPeriod>Forecast</calculationPeriod>

</period>

<generatedName>MyOutputVavable|A[t] = MyInputVavable|A[t] * a + b</generatedName>

</model>

</Item>

</its>

</calculationChain>

</visualController>

<suppressEmptyArea>SerieBounds</suppressEmptyArea>

</suppressEmptyFilter>

</metamodel>

</problemMd>

</item>

</meta>

</GetMsResult>

</soapenv:Body>

</soapenv:Envelope>

JSON request:

{
 "GetMs" : 
  {
   "tMs" : 
    {
     "id" : "CGNGLNJJAFNBFOAEAMLDKJBMDFDMIKBECLCCPAGGMMNHDHAO!M!S!CCFELIOJJAFNBFOAEGCJLMLPJNCHIHJEEHKPLONIGDEKIBJDL"
    },
   "tArg" : 
    {
     "pattern" : 
      {
       "obInst" : "false",
       "all" : "false",
       "item" : 
        {
         "key" : "89669",
         "problem" : 
          {
           "metamodel" : 
            {
             "calculationChain" : "Get",
             "calcChainPattern" : 
              {
               "modelPattern" : 
                {
                 "transform" : 
                  {
                   "outputs" : "Get",
                   "formulaCount" : "true",
                   "formulas" : 
                    {
                     "method" : 
                      {
                       "series" : "true"
                      }
                    },
                   "displayId" : "true",
                   "equationsFormula" : 
                    {
                     "method" : ""
                    },
                   "series" : "Get",
                   "kind" : "true",
                   "displaySettings" : "true",
                   "additionalAttributes" : "true",
                   "calculationType" : "true",
                   "calculationDirection" : "true",
                   "transformVariable" : 
                    {
                     "slices" : "Get",
                     "transformSlice" : 
                      {
                       "selection" : "Get"
                      }
                    }
                  },
                 "stochastic" : "true",
                 "calculationPeriod" : "true",
                 "useModelPeriod" : "true",
                 "useExistingData" : "true",
                 "treatNullsAsZeros" : "true",
                 "autoName" : "true",
                 "generatedName" : "true",
                 "period" : "true",
                 "isExclusive" : "true",
                 "useAutoPeriod" : "true"
                },
               "entryKeys" : 
                {
                 "l" : "4"
                }
              }
            }
          }
        }
      },
     "execParams" : 
      {
       "k" : "0",
       "modelKeys" : 
        {
         "l" : "4"
        },
       "scenarioKeys" : "",
       "execMethod" : "true",
       "execEvaluateSeries" : "true",
       "execIsCoefficientsSaved" : "true",
       "execStatCoefficients" : "true"
      }
    }
  }
}

JSON response:

{
 "GetMsResult" : 
  {
   "id" : 
    {
     "id" : "CGNGLNJJAFNBFOAEAMLDKJBMDFDMIKBECLCCPAGGMMNHDHAO!M!S!CCFELIOJJAFNBFOAEGCJLMLPJNCHIHJEEHKPLONIGDEKIBJDL"
    },
   "meta" : 
    {
     "item" : 
      {
       "k" : "89669",
       "id" : "MODEL_NEW",
       "n" : "MODEL_NEW",
       "vis" : "1",
       "type" : "Problem",
       "problemMd" : 
        {
         "metamodel" : 
          {
           "k" : "89670",
           "calculationChain" : 
            {
             "its" : 
              {
               "Item" : 
                {
                 "k" : "4",
                 "id" : "OBJ4",
                 "n" : "MyOutputVavable|A[t] = MyInputVavable|A[t] * a + b, 1990A1-2010A1",
                 "vis" : "1",
                 "type" : "Model",
                 "excluded" : "0",
                 "graphMeta" : "",
                 "model" : 
                  {
                   "transform" : 
                    {
                     "outputs" : 
                      {
                       "its" : 
                        {
                         "Item" : 
                          {
                           "k" : "1",
                           "id" : "VARIABLES_89670",
                           "n" : "Variables",
                           "vis" : "1",
                           "slices" : 
                            {
                             "its" : 
                              {
                               "Item" : 
                                {
                                 "k" : "0",
                                 "id" : "MyOutputVavable|A",
                                 "n" : "MyOutputVavable|A",
                                 "vis" : "1",
                                 "variableKey" : "1",
                                 "stubKey" : "89671",
                                 "selections" : 
                                  {
                                   "its" : 
                                    {
                                     "Item" : 
                                      {
                                       "id" : 
                                        {
                                         "id" : "89683"
                                        },
                                       "variant" : "2"
                                      }
                                    }
                                  },
                                 "aggregator" : "None",
                                 "parametrizedDimensions" : 
                                  {
                                   "its" : 
                                    {
                                     "Item" : 
                                      {
                                       "dimension" : "0",
                                       "parameter" : "0"
                                      }
                                    }
                                  },
                                 "unitInfo" : 
                                  {
                                   "unit" : "4294967295",
                                   "measure" : "4294967295",
                                   "baseUnit" : "4294967295",
                                   "unitsDimensionKey" : "0"
                                  },
                                 "level" : "Year"
                                }
                              }
                            },
                           "variableStubKey" : "89671",
                           "parameterID" : "",
                           "kind" : "Stub",
                           "attributeId" : "",
                           "attributeType" : "Series"
                          }
                        }
                      },
                     "formulaCount" : "1",
                     "formulas" : 
                      {
                       "its" : 
                        {
                         "it" : 
                          [
                            {
                             "k" : "0",
                             "kind" : "NonLinearRegression",
                             "method" : 
                              {
                               "nonLinearRegression" : 
                                {
                                 "missingData" : 
                                  {
                                   "specifiedVector" : "",
                                   "method" : "LinTrend",
                                   "methodParameter" : "5",
                                   "specifiedValue" : "0",
                                   "specifiedTerm" : 
                                    {
                                     "k" : "4294967295"
                                    }
                                  },
                                 "confidenceLevel" : "0.9",
                                 "useDerivatives" : "1",
                                 "initialApproximation" : 
                                  {
                                   "d" : 
                                    [
                                      "0.15",
                                      "0.09"
                                    ]
                                  },
                                 "maxIterations" : "500",
                                 "maxStep" : "0.4",
                                 "dampingFactorTolerance" : "0.6",
                                 "expression" : "@_2:0[] * a + b",
                                 "result" : 
                                  {
                                   "slice" : 
                                    {
                                     "k" : "0",
                                     "id" : "MyOutputVavable|A",
                                     "n" : "MyOutputVavable|A",
                                     "vis" : "1",
                                     "variableKey" : "1",
                                     "stubKey" : "89671",
                                     "selections" : 
                                      {
                                       "its" : 
                                        {
                                         "Item" : 
                                          {
                                           "id" : 
                                            {
                                             "id" : "89683"
                                            },
                                           "variant" : "2"
                                          }
                                        }
                                      },
                                     "aggregator" : "None",
                                     "parametrizedDimensions" : 
                                      {
                                       "its" : 
                                        {
                                         "Item" : 
                                          {
                                           "dimension" : "0",
                                           "parameter" : "0"
                                          }
                                        }
                                      },
                                     "unitInfo" : 
                                      {
                                       "unit" : "4294967295",
                                       "measure" : "4294967295",
                                       "baseUnit" : "4294967295",
                                       "unitsDimensionKey" : "0"
                                      },
                                     "level" : "Year"
                                    },
                                   "lag" : "",
                                   "key" : "0",
                                   "termToText" : "{MyOutputVavable|A[t]}",
                                   "termToInnerText" : "@_1:0[]",
                                   "termInfo" : 
                                    {
                                     "k" : "4294967295",
                                     "lag" : "0",
                                     "inversion" : 
                                      {
                                       "type" : "None",
                                       "lag" : "PrecidingValue",
                                       "previousLag" : "-1",
                                       "seasonality" : "None",
                                       "dependence" : "Linear",
                                       "K" : "3"
                                      },
                                     "slice" : 
                                      {
                                       "k" : "0",
                                       "id" : "MyOutputVavable|A",
                                       "n" : "MyOutputVavable|A",
                                       "vis" : "1",
                                       "variableKey" : "1",
                                       "stubKey" : "89671",
                                       "selections" : 
                                        {
                                         "its" : 
                                          {
                                           "Item" : 
                                            {
                                             "id" : 
                                              {
                                               "id" : "89683"
                                              },
                                             "variant" : "2"
                                            }
                                          }
                                        },
                                       "aggregator" : "None",
                                       "parametrizedDimensions" : 
                                        {
                                         "its" : 
                                          {
                                           "Item" : 
                                            {
                                             "dimension" : "0",
                                             "parameter" : "0"
                                            }
                                          }
                                        },
                                       "unitInfo" : 
                                        {
                                         "unit" : "4294967295",
                                         "measure" : "4294967295",
                                         "baseUnit" : "4294967295",
                                         "unitsDimensionKey" : "0"
                                        },
                                       "level" : "Year"
                                      },
                                     "date" : "1899-12-30"
                                    },
                                   "unitInfo" : 
                                    {
                                     "unit" : "4294967295",
                                     "measure" : "4294967295",
                                     "baseUnit" : "4294967295",
                                     "unitsDimensionKey" : "0"
                                    },
                                   "included" : "0"
                                  },
                                 "operands" : 
                                  {
                                   "its" : 
                                    {
                                     "Item" : 
                                      [
                                        {
                                         "k" : "0",
                                         "slice" : 
                                          {
                                           "k" : "0",
                                           "id" : "MyInputVavable|A",
                                           "n" : "MyInputVavable|A",
                                           "vis" : "1",
                                           "variableKey" : "2",
                                           "stubKey" : "89671",
                                           "selections" : 
                                            {
                                             "its" : 
                                              {
                                               "Item" : 
                                                {
                                                 "id" : 
                                                  {
                                                   "id" : "89683"
                                                  },
                                                 "variant" : "1"
                                                }
                                              }
                                            },
                                           "aggregator" : "None",
                                           "parametrizedDimensions" : 
                                            {
                                             "its" : 
                                              {
                                               "Item" : 
                                                {
                                                 "dimension" : "0",
                                                 "parameter" : "0"
                                                }
                                              }
                                            },
                                           "unitInfo" : 
                                            {
                                             "unit" : "4294967295",
                                             "measure" : "4294967295",
                                             "baseUnit" : "4294967295",
                                             "unitsDimensionKey" : "0"
                                            },
                                           "level" : "Year"
                                          },
                                         "lag" : "1",
                                         "key" : "1",
                                         "termToText" : "{TS(MyInputVavable|A[t+1], Linear)}",
                                         "termToInnerText" : "@_2:0[1][9:0]",
                                         "termInfo" : 
                                          {
                                           "k" : "4294967295",
                                           "lag" : "1",
                                           "inversion" : 
                                            {
                                             "type" : "TS",
                                             "lag" : "PrecidingValue",
                                             "previousLag" : "-1",
                                             "seasonality" : "None",
                                             "dependence" : "Linear",
                                             "K" : "3"
                                            },
                                           "slice" : 
                                            {
                                             "k" : "0",
                                             "id" : "MyInputVavable|A",
                                             "n" : "MyInputVavable|A",
                                             "vis" : "1",
                                             "variableKey" : "2",
                                             "stubKey" : "89671",
                                             "selections" : 
                                              {
                                               "its" : 
                                                {
                                                 "Item" : 
                                                  {
                                                   "id" : 
                                                    {
                                                     "id" : "89683"
                                                    },
                                                   "variant" : "1"
                                                  }
                                                }
                                              },
                                             "aggregator" : "None",
                                             "parametrizedDimensions" : 
                                              {
                                               "its" : 
                                                {
                                                 "Item" : 
                                                  {
                                                   "dimension" : "0",
                                                   "parameter" : "0"
                                                  }
                                                }
                                              },
                                             "unitInfo" : 
                                              {
                                               "unit" : "4294967295",
                                               "measure" : "4294967295",
                                               "baseUnit" : "4294967295",
                                               "unitsDimensionKey" : "0"
                                              },
                                             "level" : "Year"
                                            },
                                           "date" : "1899-12-30"
                                          },
                                         "unitInfo" : 
                                          {
                                           "unit" : "4294967295",
                                           "measure" : "4294967295",
                                           "baseUnit" : "4294967295",
                                           "unitsDimensionKey" : "0"
                                          },
                                         "included" : "0"
                                        },
                                        {
                                         "k" : "1",
                                         "slice" : 
                                          {
                                           "k" : "0",
                                           "id" : "MyInputVavable|A",
                                           "n" : "MyInputVavable|A",
                                           "vis" : "1",
                                           "variableKey" : "2",
                                           "stubKey" : "89671",
                                           "selections" : 
                                            {
                                             "its" : 
                                              {
                                               "Item" : 
                                                {
                                                 "id" : 
                                                  {
                                                   "id" : "89683"
                                                  },
                                                 "variant" : "1"
                                                }
                                              }
                                            },
                                           "aggregator" : "None",
                                           "parametrizedDimensions" : 
                                            {
                                             "its" : 
                                              {
                                               "Item" : 
                                                {
                                                 "dimension" : "0",
                                                 "parameter" : "0"
                                                }
                                              }
                                            },
                                           "unitInfo" : 
                                            {
                                             "unit" : "4294967295",
                                             "measure" : "4294967295",
                                             "baseUnit" : "4294967295",
                                             "unitsDimensionKey" : "0"
                                            },
                                           "level" : "Year"
                                          },
                                         "lag" : "0",
                                         "key" : "2",
                                         "termToText" : "{MyInputVavable|A[t]}",
                                         "termToInnerText" : "@_2:0[]",
                                         "termInfo" : 
                                          {
                                           "k" : "4294967295",
                                           "lag" : "0",
                                           "inversion" : 
                                            {
                                             "type" : "None",
                                             "lag" : "PrecidingValue",
                                             "previousLag" : "-1",
                                             "seasonality" : "None",
                                             "dependence" : "Linear",
                                             "K" : "3"
                                            },
                                           "slice" : 
                                            {
                                             "k" : "0",
                                             "id" : "MyInputVavable|A",
                                             "n" : "MyInputVavable|A",
                                             "vis" : "1",
                                             "variableKey" : "2",
                                             "stubKey" : "89671",
                                             "selections" : 
                                              {
                                               "its" : 
                                                {
                                                 "Item" : 
                                                  {
                                                   "id" : 
                                                    {
                                                     "id" : "89683"
                                                    },
                                                   "variant" : "1"
                                                  }
                                                }
                                              },
                                             "aggregator" : "None",
                                             "parametrizedDimensions" : 
                                              {
                                               "its" : 
                                                {
                                                 "Item" : 
                                                  {
                                                   "dimension" : "0",
                                                   "parameter" : "0"
                                                  }
                                                }
                                              },
                                             "unitInfo" : 
                                              {
                                               "unit" : "4294967295",
                                               "measure" : "4294967295",
                                               "baseUnit" : "4294967295",
                                               "unitsDimensionKey" : "0"
                                              },
                                             "level" : "Year"
                                            },
                                           "date" : "1899-12-30"
                                          },
                                         "unitInfo" : 
                                          {
                                           "unit" : "4294967295",
                                           "measure" : "4294967295",
                                           "baseUnit" : "4294967295",
                                           "unitsDimensionKey" : "0"
                                          },
                                         "included" : "1"
                                        }
                                      ]
                                    }
                                  },
                                 "coefficients" : 
                                  {
                                   "it" : 
                                    [
                                      "a",
                                      "b"
                                    ]
                                  },
                                 "isCoefficientsSaved" : "0",
                                 "statCoefficients" : 
                                  {
                                   "its" : 
                                    {
                                     "Item" : 
                                      [
                                        {
                                         "estimate" : "-0.07833068250940456",
                                         "standardError" : "0.04307364909196183",
                                         "tStatistic" : "-1.818529058036604",
                                         "probability" : "0.08900474700852867"
                                        },
                                        {
                                         "estimate" : "4.374510772763077",
                                         "standardError" : "0.6880094965630595",
                                         "tStatistic" : "6.358212778480349",
                                         "probability" : "1.285011021923133e-05"
                                        }
                                      ]
                                    }
                                  },
                                 "optimizationMethod" : "LevenbergMarquardt",
                                 "tolerance" : "0.0001",
                                 "useDefaultInitValues" : "0"
                                },
                               "name" : "X2 * (-0.0783) + 4.3745",
                               "series" : 
                                {
                                 "input" : 
                                  {
                                   "k" : "4294967295",
                                   "lag" : "0",
                                   "inversion" : 
                                    {
                                     "type" : "None",
                                     "lag" : "PrecidingValue",
                                     "previousLag" : "-1",
                                     "seasonality" : "None",
                                     "dependence" : "Linear",
                                     "K" : "3"
                                    },
                                   "slice" : 
                                    {
                                     "k" : "0",
                                     "id" : "MyOutputVavable|A",
                                     "n" : "MyOutputVavable|A",
                                     "vis" : "1",
                                     "variableKey" : "1",
                                     "stubKey" : "89671",
                                     "selections" : 
                                      {
                                       "its" : 
                                        {
                                         "Item" : 
                                          {
                                           "id" : 
                                            {
                                             "id" : "89683"
                                            },
                                           "variant" : "2"
                                          }
                                        }
                                      },
                                     "aggregator" : "None",
                                     "parametrizedDimensions" : 
                                      {
                                       "its" : 
                                        {
                                         "Item" : 
                                          {
                                           "dimension" : "0",
                                           "parameter" : "0"
                                          }
                                        }
                                      },
                                     "unitInfo" : 
                                      {
                                       "unit" : "4294967295",
                                       "measure" : "4294967295",
                                       "baseUnit" : "4294967295",
                                       "unitsDimensionKey" : "0"
                                      },
                                     "level" : "Year"
                                    },
                                   "date" : "1899-12-30"
                                  },
                                 "addFactor" : 
                                  {
                                   "k" : "4294967295"
                                  }
                                },
                               "evaluateSeries" : 
                                {
                                 "its" : 
                                  {
                                   "Item" : 
                                    {
                                     "scenarioKey" : "4294967295",
                                     "fact" : 
                                      {
                                       "d" : 
                                        [
                                          "3",
                                          "7",
                                          "2",
                                          "6",
                                          "4",
                                          "1",
                                          "5",
                                          "3.42857143",
                                          "3.28571429",
                                          "3.14285714",
                                          "3",
                                          "2.85714286",
                                          "2.71428571",
                                          "2.57142857",
                                          "2.42857143",
                                          "2.28571429",
                                          "2.14285714"
                                        ]
                                      },
                                     "modelling" : 
                                      {
                                       "d" : 
                                        [
                                          "4.296180090253672",
                                          "4.061188042725458",
                                          "4.217849407744268",
                                          "3.826195995197245",
                                          "3.787030653942542",
                                          "3.661701561927495",
                                          "3.536372469912448",
                                          "3.4110433778974",
                                          "3.285714285882353",
                                          "3.160385193867306",
                                          "3.035056101852258",
                                          "2.909727009837211",
                                          "2.784397917822164",
                                          "2.659068825807117",
                                          "2.53373973379207",
                                          "2.408410641777022",
                                          "2.283081549761975"
                                        ]
                                      },
                                     "residuals" : 
                                      {
                                       "d" : 
                                        [
                                          "-1.296180090253672",
                                          "2.938811957274542",
                                          "-2.217849407744268",
                                          "2.173804004802755",
                                          "0.2129693460574575",
                                          "-2.661701561927495",
                                          "1.463627530087552",
                                          "0.01752805210259956",
                                          "4.117647112167333e-09",
                                          "-0.01752805386730616",
                                          "-0.03505610185225816",
                                          "-0.05258414983721105",
                                          "-0.07011220782216387",
                                          "-0.08764025580711676",
                                          "-0.1051683037920697",
                                          "-0.1226963517770217",
                                          "-0.1402244097619749"
                                        ]
                                      },
                                     "input" : 
                                      {
                                       "d" : 
                                        [
                                          "3",
                                          "7",
                                          "2",
                                          "6",
                                          "4",
                                          "1",
                                          "5",
                                          "3.42857143",
                                          "3.28571429",
                                          "3.14285714",
                                          "3",
                                          "2.85714286",
                                          "2.71428571",
                                          "2.57142857",
                                          "2.42857143",
                                          "2.28571429",
                                          "2.14285714",
                                          "2",
                                          "1.85714286",
                                          "1.71428571",
                                          "1.57142857"
                                        ]
                                      },
                                     "factors" : 
                                      {
                                       "its" : 
                                        {
                                         "it" : 
                                          [
                                            {
                                             "termToText" : "{MyInputVavable|A[t]}",
                                             "serie" : 
                                              {
                                               "d" : 
                                                [
                                                  "1",
                                                  "4",
                                                  "2",
                                                  "7",
                                                  "7.5",
                                                  "9.1",
                                                  "10.7",
                                                  "12.3",
                                                  "13.9",
                                                  "15.5",
                                                  "17.1",
                                                  "18.7",
                                                  "20.3",
                                                  "21.9",
                                                  "23.5",
                                                  "25.1",
                                                  "26.7",
                                                  "28.3",
                                                  "29.9",
                                                  "31.5",
                                                  "33.1"
                                                ]
                                              },
                                             "inversion" : 
                                              {
                                               "type" : "None",
                                               "lag" : "PrecidingValue",
                                               "previousLag" : "-1",
                                               "seasonality" : "None",
                                               "dependence" : "Linear",
                                               "K" : "3"
                                              },
                                             "entryKey" : "1"
                                            }
                                          ]
                                        }
                                      }
                                    }
                                  },
                                 "dates" : 
                                  {
                                   "it" : 
                                    [
                                      "1990A1",
                                      "1991A1",
                                      "1992A1",
                                      "1993A1",
                                      "1994A1",
                                      "1995A1",
                                      "1996A1",
                                      "1997A1",
                                      "1998A1",
                                      "1999A1",
                                      "2000A1",
                                      "2001A1",
                                      "2002A1",
                                      "2003A1",
                                      "2004A1",
                                      "2005A1",
                                      "2006A1",
                                      "2007A1",
                                      "2008A1",
                                      "2009A1",
                                      "2010A1"
                                    ]
                                  }
                                },
                               "inversionInfo" : 
                                {
                                 "type" : "None",
                                 "lag" : "PrecidingValue",
                                 "previousLag" : "-1",
                                 "seasonality" : "None",
                                 "dependence" : "Linear",
                                 "K" : "3"
                                },
                               "doUseR" : "0",
                               "supportsR" : "1"
                              },
                             "calendarLevel" : "Year",
                             "outputSliceKey" : "0"
                            }
                          ]
                        }
                      },
                     "displayId" : "0",
                     "series" : 
                      {
                       "its" : ""
                      },
                     "kind" : "Simple",
                     "displaySettings" : 
                      {
                       "displayTermsAs" : "Derive"
                      },
                     "additionalAttributes" : "",
                     "calculationType" : "Serie",
                     "calculationDirection" : "Forward"
                    },
                   "stochastic" : "1",
                   "calculationPeriod" : "Forecast",
                   "useModelPeriod" : "1",
                   "useExistingData" : "0",
                   "treatNullsAsZeros" : "0",
                   "autoName" : "1",
                   "period" : 
                    {
                     "identificationStartDate" : "1990-01-01",
                     "identificationEndDate" : "2006-01-01",
                     "forecastStartDate" : "2006-01-02",
                     "forecastEndDate" : "2010-01-01",
                     "identificationStartDateParamID" : "",
                     "identificationEndDateParamID" : "",
                     "forecastStartDateParamID" : "",
                     "forecastEndDateParamID" : "",
                     "autoPeriod" : "0",
                     "identificationStartOffset" : "0",
                     "identificationEndOffset" : "0",
                     "forecastEndOffset" : "0",
                     "isIdentStartCorrect" : "1",
                     "isIdentEndCorrect" : "1",
                     "isForecastEndCorrect" : "1"
                    },
                   "isExclusive" : "1",
                   "useAutoPeriod" : "0",
                   "generatedName" : "MyOutputVavable|A[t] = MyInputVavable|A[t] * a + b",
                   "warnings" : "",
                   "readOnly" : "0"
                  }
                }
              }
            },
           "visualController" : 
            {
             "userRPath" : "",
             "isRExist" : "0"
            },
           "suppressEmptyFilter" : 
            {
             "suppressEmpty" : "0",
             "suppressEmptyArea" : "SerieBounds"
            },
           "readOnly" : "0",
           "variableTestUseR" : "0",
           "calculateIdentOnFact" : "0"
          },
         "useScenarios" : "0",
         "readOnly" : "0"
        }
      }
    }
  }
}

The GetMsNonLinearRegr function calculates the specified equation. Input parameters:

ms. Opened modeling container instance.
modelKey. Key of the model that contains the equation.
eqKey. Equation key.

After executing the function returns a model that contains calculated equation. Calculation results are displayed in the console window. The following auxiliary procedures described in the Calculating Equation section are used to output the results: PrintArray and PrintSeries.

public static MsCalculationChainEntry GetMsNonLinearRegr(MsId ms, ulong modelKey, ulong eqKey)
{
    var getMsOp = new GetMs();
    // Set operation execution parameters
    getMsOp.tMs = ms;
    getMsOp.tArg = new GetMsArg()
    {  // Set data extraction pattern
        pattern = new MsMdPattern()
        {
            obInst = false,
            all = false,
            item = new MsItemPattern()
            {  // Specify calculated model class
                key = modelKey,
                problem = new MsProblemPattern()
                {
                    metamodel = new MsMetaModelPattern()
                    {
                        calculationChain = ListOperation.Get,
                        calcChainPattern = new MsCalculationChainPattern()
                        {
                            // Specify calculated equation key
                            entryKeys = new long[] { (long)eqKey },
                            modelPattern = new MsModelPattern()
                            {
                                autoName = true,
                                calculationPeriod = true,
                                generatedName = true,
                                isExclusive = true,
                                period = true,
                                stochastic = true,
                                treatNullsAsZeros = true,
                                useAutoPeriod = true,
                                useExistingData = true,
                                useModelPeriod = true,
                                transform = new MsFormulaTransformPattern()
                                {
                                    additionalAttributes = true,
                                    calculationDirection = true,
                                    calculationType = true,
                                    displayId = true,
                                    displaySettings = true,
                                    formulaCount = true,
                                    outputs = ListOperation.Get,
                                    series = ListOperation.Get,
                                    kind = true,
                                    formulas = new TsFormulaPattern()
                                    {
                                        method = new TsMethodPattern()
                                        {
                                            series = true
                                        }
                                    },
                                    equationsFormula = new TsFormulaPattern()
                                    {
                                        method = new TsMethodPattern() { }
                                    },
                                    transformVariable = new MsFormulaTransformVariablePattern()
                                    {
                                        slices = ListOperation.Get,
                                        transformSlice = new MsFormulaTransformSlicePattern()
                                        {
                                            selection = ListOperation.Get
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }, // Set equation calculation parameters
        execParams = new MsMdExecParams()
        {
            k = 0,
            execMethod = true,
            execEvaluateSeries = true,
            scenarioKeys = new long[] { },            
            execStatCoefficients = true,
            execIsCoefficientsSaved = true,
            modelKeys = new long[] { (long)eqKey }
        }
    };
    // Create a proxy object for operation execution
    var somClient = new SomPortTypeClient();
    GetMsResult getMsResult = somClient.GetMs(getMsOp);
    MsMetaModel meta = getMsResult.meta.item.problemMd.metamodel;
    MsCalculationChainEntry chainEntry = meta.calculationChain.its.GetValue(0) as MsCalculationChainEntry;
    // Display errors and warnings
    MsModel eq = chainEntry.model;
    if (eq.warnings != null)
    {
        Console.WriteLine(&quot;-- Warnings --&quot;);
        Console.WriteLine(&quot;&quot;.PadRight(3) + printArray(eq.warnings));
    }
    if (eq.error == null) //Check if errors occurred on equation calculation
    {   // Equation is calculated without errors, get calculation results   
        TsFormula formula = eq.transform.formulas.its.GetValue(0) as TsFormula;
        TsNonLinearRegressionMethod nonLinR = formula.method.nonLinearRegression;
        Console.WriteLine(&quot;-- Coefficients --&quot;);
        Console.WriteLine(&quot;&quot;.PadRight(3) + printArray(nonLinR.coefficients));
        Console.WriteLine(&quot;&quot;.PadRight(3) + &quot;- saved: &quot; + nonLinR.isCoefficientsSaved);
        Console.WriteLine(&quot;-- Coefficient values --&quot;);
        Console.WriteLine(&quot;&quot;.PadRight(3) + printArray(nonLinR.coefficientsData));
        // Get equation coefficient values and display into console window
        Console.WriteLine(&quot;-- Detailed description of coefficients --&quot;);
        StatConstCoefficientsArr cArr = nonLinR.statCoefficients;
        Console.WriteLine(&quot;&quot;.PadRight(3) + &quot;- accuracy of solution: &quot; + cArr.precision);
        int i = 0;
        foreach (StatConstCoefficients n in cArr.its)
        {
            Console.WriteLine(&quot;&quot;.PadRight(3) + &quot;Coefficient '&quot; + nonLinR.coefficients.GetValue(i) + &quot;'&quot;);
            Console.WriteLine(&quot;&quot;.PadRight(6) + &quot; - value: &quot; + n.estimate);
            Console.WriteLine(&quot;&quot;.PadRight(6) + &quot; - standard error: &quot; + n.standardError);
            Console.WriteLine(&quot;&quot;.PadRight(6) + &quot; - t-statistics: &quot; + n.tStatistic);
            Console.WriteLine(&quot;&quot;.PadRight(6) + &quot; - probability: &quot; + n.probability);
            i++;
        }     
        // Get calculated values and display into console window
        MsEvaluateSeriesResult seriesRes = formula.method.evaluateSeries;
        printSeries(seriesRes);
    }
    else // Errors occurred on equation calculation
    {
        Console.WriteLine(&quot;-- Errors --&quot;);
        Console.WriteLine(eq.error);
    }
    // Return the model that contains equation
    return chainEntry;
}