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--- visual3d:documentation:statistics:compute_linear_regression [2024/06/19 12:53] – sgranger
+++ visual3d:documentation:statistics:compute_linear_regression [2024/07/17 15:46] (current) – created sgranger
@@ Line 1: / Line 1: @@
-{{{{{{since this page was created a command has been added to visual3d.
+====== Compute Linear Regression ======
-[[visual3d:documentation:pipeline:metric_commands:metric_to_fit_signal_to_line|metric_to_fit_signal_to_line]]
+Since this page was created a command has been added to Visual3D.
-this example uses a command script that calls a meta-command that will compute a linear regression of the data identified in the script. see also [[visual3d:documentation:statistics:meta_command_for_linear_regression|statistics_example_5]] for another example.
-given the following definition of a linear regression:
+[[Visual3D:Documentation:Pipeline:Metric_Commands:Metric_To_Fit_Signal_To_Line|Metric_To_Fit_Signal_To_Line]]
+This example uses a command script that calls a meta-command that will compute a linear regression of the data identified in the script. See also [[Visual3D:Documentation:Statistics:Meta_Command_for_Linear_Regression|Statistics_Example_5]] for another example.
+Given the following definition of a linear regression:
 <code>
-regression equation: y = b + mx
+Regression Equation: y = b + mx
-slope: m = (nσxy - (σx)(σy)) / (nσx^2 - (σx)^2)
+Slope: m = (NΣXY - (ΣX)(ΣY)) / (NΣX^2 - (ΣX)^2)
-intercept: b = (σy - m(σx)) / n
+Intercept: b = (ΣY - m(ΣX)) / N
 where :
   x and y are the variables.
-  m = the slope of the regression line
+  m = The slope of the regression line
-  b = the intercept point of the regression line and the y axis.
+  b = The intercept point of the regression line and the y axis.
-  n = number of values or elements
+  N = Number of values or elements
-  x = array of x-components
+  X = array of x-components
-  y = array of y-components
+  Y = array of y-components
-  σx = sum of x
+  ΣX = Sum of x
-  σy = sum of y
+  ΣY = Sum of y
-  σxy = sum of xy
+  ΣXY = Sum of xy
-  σx^2 = sum of x^2
+  ΣX^2 = Sum of x^2
 </code>
-===== example data =====
+==== Example Data ====
-given the following data:
+Given the following data:
 |5 ||3.1|
@@ Line 38: / Line 40: @@
 |11||4.7|
-===== linear_regression_explicit pipeline script =====
+==== Linear_Regression_Explicit Pipeline Script ====
-this pipeline command script creates the signals and calls the **linear_regression_explicit** meta command.
+This pipeline command script creates the signals and calls the **linear_regression_explicit** meta command.
 <code>
 !=========================================================================
-! this script will call the meta-command linear_regression_explicit that
+! This script will call the meta-command linear_regression_explicit that
-! will perform a linear regression of data that is placed in the global
+! will perform a linear regression of data that is placed in the GLOBAL
 !
-! note: regression equation: y = b + mx
+! Note: Regression Equation: y = b + mx
 !
-! slope: m = (nσxy - (σx)(σy)) / (nσx^2 - (σx)^2)
+! Slope: m = (NΣXY - (ΣX)(ΣY)) / (NΣX^2 - (ΣX)^2)
 !
-! intercept: b = (σy - m(σx)) / n
+! Intercept: b = (ΣY - m(ΣX)) / N
 !
 ! where :
 !
 !  x and y are the variables.
-!  m = the slope of the regression line
+!  m = The slope of the regression line
-!  b = the intercept point of the regression line and the y axis.
+!  b = The intercept point of the regression line and the y axis.
-!  n = number of values or elements
+!  N = Number of values or elements
-!  x = array of x-components
+!  X = array of x-components
-!  y = array of y-components
+!  Y = array of y-components
-!  σx = sum of x
+!  ΣX = Sum of x
-!  σy = sum of y
+!  ΣY = Sum of y
-!  σxy = sum of xy
+!  ΣXY = Sum of xy
-!  σx^2 = sum of x^2
+!  ΣX^2 = Sum of x^2
 !=========================================================================
-! the global needs to be active
+! The GLOBAL needs to be active
-select_active_file
+Select_Active_File
-/file_name=global
+/FILE_NAME=GLOBAL
-! /query=
+! /QUERY=
 ;
 !-------------------------------------------------------
-! create a signal containing the number of data points
+! Create a signal containing the number of data points
 !-------------------------------------------------------
-metric_explicit
+Metric_Explicit
-/result_metric_name=n
+/RESULT_METRIC_NAME=N
-/result_metric_folder=residual
+/RESULT_METRIC_FOLDER=RESIDUAL
-/metric_value=6
+/METRIC_VALUE=6
 ;
 ! create a signal containing the data
-evaluate_expression
+Evaluate_Expression
-/expression=list(vector(5,3.1),vector(6,3.5),vector(7,3.9),vector(9,4.1),vector(10,4.3),vector(11,4.7))
+/EXPRESSION=LIST(VECTOR(5,3.1),VECTOR(6,3.5),VECTOR(7,3.9),VECTOR(9,4.1),VECTOR(10,4.3),VECTOR(11,4.7))
-/result_name=test
+/RESULT_NAME=TEST
-/result_type=derived
+/RESULT_TYPE=DERIVED
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
 !--------------------------------------------------
-! call the meta command linear_regression_explicit
+! Call the meta command linear_regression_explicit
 !--------------------------------------------------
 linear_regression_explicit
-/signalx=derived::residual::test::x
+/SIGNALX=DERIVED::RESIDUAL::TEST::X
-/signaly=derived::residual::test::y
+/SIGNALY=DERIVED::RESIDUAL::TEST::Y
-/num_points= metric::residual::n
+/NUM_POINTS= METRIC::RESIDUAL::N
-/result_name=result
+/RESULT_NAME=RESULT
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
 !--------------------------------------------------------------------------
 ! create signal representing the linear regression
-! 4 temporary signals are created for clarity - startx, endx, starty, endy
+! 4 temporary signals are created for clarity - STARTX, ENDX, STARTY, ENDY
 !--------------------------------------------------------------------------
-! create startx at the first datapoint
+! Create STARTX at the first datapoint
-evaluate_expression
+Evaluate_Expression
-/expression=derived::residual::test::x[1]
+/EXPRESSION=DERIVED::RESIDUAL::TEST::X[1]
-/result_name=startx
+/RESULT_NAME=STARTX
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
-! create endx at the nth datapoint
+! Create ENDX at the Nth datapoint
-evaluate_expression
+Evaluate_Expression
-/expression=derived::residual::test::x[metric::residual::n]
+/EXPRESSION=DERIVED::RESIDUAL::TEST::X[METRIC::RESIDUAL::N]
-/result_name=endx
+/RESULT_NAME=ENDX
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
-! create starty from the meta command regression results and startx (y = b + mx)
+! Create STARTY from the meta command regression results and STARTX (y = b + mx)
-evaluate_expression
+Evaluate_Expression
-/expression=metric::residual::result::x+metric::residual::result::y*metric::residual::startx
+/EXPRESSION=METRIC::RESIDUAL::RESULT::X+METRIC::RESIDUAL::RESULT::Y*METRIC::RESIDUAL::STARTX
-/result_name=starty
+/RESULT_NAME=STARTY
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
-! create endy from the meta command regression results and endx (y = b + mx)
+! Create ENDY from the meta command regression results and ENDX (y = b + mx)
-evaluate_expression
+Evaluate_Expression
-/expression=metric::residual::result::x+metric::residual::result::y*metric::residual::endx
+/EXPRESSION=METRIC::RESIDUAL::RESULT::X+METRIC::RESIDUAL::RESULT::Y*METRIC::RESIDUAL::ENDX
-/result_name=endy
+/RESULT_NAME=ENDY
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
-! create the line
+! Create the line
-evaluate_expression
+Evaluate_Expression
-/expression=list(vector(metric::residual::startx,metric::residual::starty),vector(metric::residual::endx,metric::residual::endy))
+/EXPRESSION=LIST(VECTOR(METRIC::RESIDUAL::STARTX,METRIC::RESIDUAL::STARTY),VECTOR(METRIC::RESIDUAL::ENDX,METRIC::RESIDUAL::ENDY))
-/result_name=result_line
+/RESULT_NAME=RESULT_LINE
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
 </code>
-===== graph the data and regression line =====
+==== Graph the Data and Regression Line ====
-the resulting signal **metric::residual::result_line** can be graphed in a report graph with the original data.
+The resulting signal **METRIC::RESIDUAL::RESULT_LINE** can be graphed in a report graph with the original data.
-for example, create a report graph (2d graph) as follows:
+For example, create a report graph (2D Graph) as follows:
-linear_regression1.jpg
+{{:Linear_regression1.jpg}}
-now create a second 2d graph at the same location containing the regression line
+Now create a second 2D graph at the same location containing the regression line
-linear_regression2.jpg
+{{:Linear_regression2.jpg}}
-the resulting report graph should appear as follows:
+The resulting report graph should appear as follows:
-linear_regression3.jpg
+{{:Linear_regression3.jpg}}
-===== linear_regression_explicit meta-command =====
+==== Linear_Regression_Explicit Meta-Command ====
-below are the commands for the **linear_regression_explicit** meta-commands. go to [[visual3d:documentation:pipeline:meta_commands:meta_commands_overview|pipeline commands:meta commands]] for details on how to use meta-commands.
+Below are the commands for the **Linear_Regression_Explicit** Meta-Commands. Go to [[Visual3D:Documentation:Pipeline:Meta_Commands:Meta_Commands_Overview|Pipeline Commands:Meta Commands]] for details on how to use Meta-commands.
 <code>
-! begin_meta
+! BEGIN_META
-! meta_cmd_name=linear_regression_explicit
+! META_CMD_NAME=Linear_Regression_Explicit
-! meta_param= signalx  : string ::yes
+! META_PARAM= SIGNALX  : string ::yes
-! meta_param= signaly  : string ::yes
+! META_PARAM= SIGNALY  : string ::yes
-! meta_param= num_points  : string ::yes
+! META_PARAM= NUM_POINTS  : string ::yes
-! meta_param= result_name  : string ::yes
+! META_PARAM= RESULT_NAME  : string ::yes
-! meta_param= result_folder  : string ::yes
+! META_PARAM= RESULT_FOLDER  : string ::yes
-! end_meta
+! END_META
 !========================================================================
-! this meta-command will calculate the linear regression of data
+! This meta-command will calculate the linear regression of data
 ! that is passed to the meta-command
 !
-! note: regression equation: y = b + mx
+! Note: Regression Equation: y = b + mx
 !
-! slope: m = (nσxy - (σx)(σy)) / (nσx^2 - (σx)^2)
+! Slope: m = (NΣXY - (ΣX)(ΣY)) / (NΣX^2 - (ΣX)^2)
 !
-! intercept: b = (σy - m(σx)) / n
+! Intercept: b = (ΣY - m(ΣX)) / N
 !
 ! where :
 !
 !  x and y are the variables.
-!  m = the slope of the regression line
+!  m = The slope of the regression line
-!  b = the intercept point of the regression line and the y axis.
+!  b = The intercept point of the regression line and the y axis.
-!  n = number of values or elements
+!  N = Number of values or elements
-!  x = array of x-components
+!  X = array of x-components
-!  y = array of y-components
+!  Y = array of y-components
-!  σx = sum of x
+!  ΣX = Sum of x
-!  σy = sum of y
+!  ΣY = Sum of y
-!  σxy = sum of xy
+!  ΣXY = Sum of xy
-!  σx^2 = sum of x^2
+!  ΣX^2 = Sum of x^2
 !==========================================================================
 !---------------------------------------------------------------------------
-! create temporary variables - tempx and tempy from signal::x and signal::y
+! Create Temporary Variables - TEMPX and TEMPY from SIGNAL::X and SIGNAL::Y
 !---------------------------------------------------------------------------
-set_pipeline_parameter
+Set_Pipeline_Parameter
-/parameter_name=name
+/PARAMETER_NAME=NAME
-/parameter_value=::result_name
+/PARAMETER_VALUE=::RESULT_NAME
 ;
-set_pipeline_parameter
+Set_Pipeline_Parameter
-/parameter_name=folder
+/PARAMETER_NAME=FOLDER
-/parameter_value=::result_folder
+/PARAMETER_VALUE=::RESULT_FOLDER
 ;
-! create tempx
+! Create TEMPX
-evaluate_expression
+Evaluate_Expression
-/expression=::signalx
+/EXPRESSION=::SIGNALX
-/result_name=tempx
+/RESULT_NAME=TEMPX
-/result_type=derived
+/RESULT_TYPE=DERIVED
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
-! create tempy
+! Create TEMPY
-evaluate_expression
+Evaluate_Expression
-/expression=::signaly
+/EXPRESSION=::SIGNALY
-/result_name=tempy
+/RESULT_NAME=TEMPY
-/result_type=derived
+/RESULT_TYPE=DERIVED
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
 !----------------------------
-! sum x and y
+! Sum X and Y
 !----------------------------
-! sum x
+! Sum X
-metric_sum
+Metric_Sum
-/result_metric_name=sumx
+/RESULT_METRIC_NAME=SUMX
-/apply_as_suffix_to_signal_name=false
+/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
-/result_metric_folder=residual
+/RESULT_METRIC_FOLDER=RESIDUAL
-/signal_types=derived
+/SIGNAL_TYPES=DERIVED
-/signal_names=tempx
+/SIGNAL_NAMES=TEMPX
-/signal_folder=residual
+/SIGNAL_FOLDER=RESIDUAL
-/signal_components=x
+/SIGNAL_COMPONENTS=X
-/event_sequence=
+/EVENT_SEQUENCE=
-/exclude_events=
+/EXCLUDE_EVENTS=
-/generate_mean_and_stddev=false
+/GENERATE_MEAN_AND_STDDEV=FALSE
-/append_to_existing_values=false
+/APPEND_TO_EXISTING_VALUES=FALSE
 ;
-! sum y
+! Sum Y
-metric_sum
+Metric_Sum
-/result_metric_name=sumy
+/RESULT_METRIC_NAME=SUMY
-/apply_as_suffix_to_signal_name=false
+/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
-/result_metric_folder=residual
+/RESULT_METRIC_FOLDER=RESIDUAL
-/signal_types=derived
+/SIGNAL_TYPES=DERIVED
-/signal_names=tempy
+/SIGNAL_NAMES=TEMPY
-/signal_folder=residual
+/SIGNAL_FOLDER=RESIDUAL
-/signal_components=x
+/SIGNAL_COMPONENTS=X
-/event_sequence=
+/EVENT_SEQUENCE=
-/exclude_events=
+/EXCLUDE_EVENTS=
-/generate_mean_and_stddev=false
+/GENERATE_MEAN_AND_STDDEV=FALSE
-/append_to_existing_values=false
+/APPEND_TO_EXISTING_VALUES=FALSE
 ;
 !----------------------
-! multiply x and y
+! Multiply X and Y
 !----------------------
-evaluate_expression
+Evaluate_Expression
-/expression=derived::residual::tempx*derived::residual::tempy
+/EXPRESSION=DERIVED::RESIDUAL::TEMPX*DERIVED::RESIDUAL::TEMPY
-/result_name=xy
+/RESULT_NAME=XY
-/result_type=derived
+/RESULT_TYPE=DERIVED
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
 !----------------------
-! sum xy
+! Sum XY
 !----------------------
-metric_sum
+Metric_Sum
-/result_metric_name=sumxy
+/RESULT_METRIC_NAME=SUMXY
-/apply_as_suffix_to_signal_name=false
+/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
-/result_metric_folder=residual
+/RESULT_METRIC_FOLDER=RESIDUAL
-/signal_types=derived
+/SIGNAL_TYPES=DERIVED
-/signal_names=xy
+/SIGNAL_NAMES=XY
-/signal_folder=residual
+/SIGNAL_FOLDER=RESIDUAL
-/signal_components=x
+/SIGNAL_COMPONENTS=X
-/event_sequence=
+/EVENT_SEQUENCE=
-/exclude_events=
+/EXCLUDE_EVENTS=
-/generate_mean_and_stddev=false
+/GENERATE_MEAN_AND_STDDEV=FALSE
-/append_to_existing_values=false
+/APPEND_TO_EXISTING_VALUES=FALSE
 ;
 !---------------
-! square x
+! Square X
 !---------------
-evaluate_expression
+Evaluate_Expression
-/expression=derived::residual::tempx*derived::residual::tempx
+/EXPRESSION=DERIVED::RESIDUAL::TEMPX*DERIVED::RESIDUAL::TEMPX
-/result_name=xx
+/RESULT_NAME=XX
-/result_type=derived
+/RESULT_TYPE=DERIVED
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
 !-----------------
-! sum square of x
+! Sum square of X
 !-----------------
-metric_sum
+Metric_Sum
-/result_metric_name=sumxx
+/RESULT_METRIC_NAME=SUMXX
-/apply_as_suffix_to_signal_name=false
+/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
-/result_metric_folder=residual
+/RESULT_METRIC_FOLDER=RESIDUAL
-/signal_types=derived
+/SIGNAL_TYPES=DERIVED
-/signal_names=xx
+/SIGNAL_NAMES=XX
-/signal_folder=residual
+/SIGNAL_FOLDER=RESIDUAL
-/signal_components=x
+/SIGNAL_COMPONENTS=X
-/event_sequence=
+/EVENT_SEQUENCE=
-/exclude_events=
+/EXCLUDE_EVENTS=
-/generate_mean_and_stddev=false
+/GENERATE_MEAN_AND_STDDEV=FALSE
-/append_to_existing_values=false
+/APPEND_TO_EXISTING_VALUES=FALSE
 ;
 !------------------
-! calculate slope
+! Calculate slope
 !------------------
-evaluate_expression
+Evaluate_Expression
-/expression=(&::num_points&*metric::residual::sumxy-metric::residual::sumx*metric::residual::sumy)/(&::num_points&*metric::residual::sumxx-metric::residual::sumx^2)
+/EXPRESSION=(&::NUM_POINTS&*METRIC::RESIDUAL::SUMXY-METRIC::RESIDUAL::SUMX*METRIC::RESIDUAL::SUMY)/(&::NUM_POINTS&*METRIC::RESIDUAL::SUMXX-METRIC::RESIDUAL::SUMX^2)
-/result_name=slope
+/RESULT_NAME=SLOPE
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
 !----------------------
-! calculate intercept
+! Calculate intercept
 !----------------------
-evaluate_expression
+Evaluate_Expression
-/expression=(metric::residual::sumy-metric::residual::slope*metric::residual::sumx)/&::num_points
+/EXPRESSION=(METRIC::RESIDUAL::SUMY-METRIC::RESIDUAL::SLOPE*METRIC::RESIDUAL::SUMX)/&::NUM_POINTS
-/result_name=intercept
+/RESULT_NAME=INTERCEPT
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=residual
+/RESULT_FOLDER=RESIDUAL
 ;
@@ Line 342: / Line 344: @@
 ! create the resulting metric signal that contains the slope and intercept
 !--------------------------------------------------------------------------
-evaluate_expression
+Evaluate_Expression
-/expression=vector(metric::residual::intercept,metric::residual::slope)
+/EXPRESSION=VECTOR(METRIC::RESIDUAL::INTERCEPT,METRIC::RESIDUAL::SLOPE)
-/result_name=::name
+/RESULT_NAME=::NAME
-/result_type=metric
+/RESULT_TYPE=METRIC
-/result_folder=::folder
+/RESULT_FOLDER=::FOLDER
 ;
@@ Line 354: / Line 356: @@
 ! comment out this next command
 !-----------------------------------------------------------
-remove_signals
+Remove_Signals
-/signal_types=derived+derived+derived+derived+metric+metric+metric+metric+metric+metric
+/SIGNAL_TYPES=DERIVED+DERIVED+DERIVED+DERIVED+METRIC+METRIC+METRIC+METRIC+METRIC+METRIC
-/signal_names=tempx+tempy+xx+xy+slope+intercept+sumx+sumxx+sumxy+sumy
+/SIGNAL_NAMES=TEMPX+TEMPY+XX+XY+SLOPE+INTERCEPT+SUMX+SUMXX+SUMXY+SUMY
-/signal_folder=residual+residual+residual+residual+residual+residual+residual+residual+residual+residual
+/SIGNAL_FOLDER=RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL
 ;
 </code>
-}}}}}}