Statistics Example 4
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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 Statistics_Example_5 for another example.
Given the following definition of a linear regression:
Regression Equation: y = b + mx Slope: m = (NΣXY - (ΣX)(ΣY)) / (NΣX^2 - (ΣX)^2) Intercept: b = (ΣY - m(ΣX)) / N where : x and y are the variables. m = The slope of the regression line b = The intercept point of the regression line and the y axis. N = Number of values or elements X = array of x-components Y = array of y-components ΣX = Sum of x ΣY = Sum of y ΣXY = Sum of xy ΣX^2 = Sum of x^2
Example Data
Given the following data:
| 5 | 3.1 | |
| 6 | 3.5 | |
| 7 | 3.9 | |
| 9 | 4.1 | |
| 10 | 4.3 | |
| 11 | 4.7 |
Linear_Regression_Explicit Pipeline Script
This pipeline command script creates the signals and calls the linear_regression_explicit meta command.
!========================================================================= ! This script will call the meta-command linear_regression_explicit that ! will perform a linear regression of data that is placed in the GLOBAL ! ! Note: Regression Equation: y = b + mx ! ! Slope: m = (NΣXY - (ΣX)(ΣY)) / (NΣX^2 - (ΣX)^2) ! ! Intercept: b = (ΣY - m(ΣX)) / N ! ! where : ! ! x and y are the variables. ! m = The slope of the regression line ! b = The intercept point of the regression line and the y axis. ! N = Number of values or elements ! X = array of x-components ! Y = array of y-components ! ΣX = Sum of x ! ΣY = Sum of y ! ΣXY = Sum of xy ! ΣX^2 = Sum of x^2 !========================================================================= ! The GLOBAL needs to be active Select_Active_File /FILE_NAME=GLOBAL ! /QUERY= ; !------------------------------------------------------- ! Create a signal containing the number of data points !------------------------------------------------------- Metric_Explicit /RESULT_METRIC_NAME=N /RESULT_METRIC_FOLDER=RESIDUAL /METRIC_VALUE=6 ; ! create a signal containing the data 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)) /RESULT_NAME=TEST /RESULT_TYPE=DERIVED /RESULT_FOLDER=RESIDUAL ; !-------------------------------------------------- ! Call the meta command linear_regression_explicit !-------------------------------------------------- linear_regression_explicit /SIGNALX=DERIVED::RESIDUAL::TEST::X /SIGNALY=DERIVED::RESIDUAL::TEST::Y /NUM_POINTS= METRIC::RESIDUAL::N /RESULT_NAME=RESULT /RESULT_FOLDER=RESIDUAL ; !-------------------------------------------------------------------------- ! create signal representing the linear regression ! 4 temporary signals are created for clarity - STARTX, ENDX, STARTY, ENDY !-------------------------------------------------------------------------- ! Create STARTX at the first datapoint Evaluate_Expression /EXPRESSION=DERIVED::RESIDUAL::TEST::X[1] /RESULT_NAME=STARTX /RESULT_TYPE=METRIC /RESULT_FOLDER=RESIDUAL ; ! Create ENDX at the Nth datapoint Evaluate_Expression /EXPRESSION=DERIVED::RESIDUAL::TEST::X[METRIC::RESIDUAL::N] /RESULT_NAME=ENDX /RESULT_TYPE=METRIC /RESULT_FOLDER=RESIDUAL ; ! Create STARTY from the meta command regression results and STARTX (y = b + mx) Evaluate_Expression /EXPRESSION=METRIC::RESIDUAL::RESULT::X+METRIC::RESIDUAL::RESULT::Y*METRIC::RESIDUAL::STARTX /RESULT_NAME=STARTY /RESULT_TYPE=METRIC /RESULT_FOLDER=RESIDUAL ; ! Create ENDY from the meta command regression results and ENDX (y = b + mx) Evaluate_Expression /EXPRESSION=METRIC::RESIDUAL::RESULT::X+METRIC::RESIDUAL::RESULT::Y*METRIC::RESIDUAL::ENDX /RESULT_NAME=ENDY /RESULT_TYPE=METRIC /RESULT_FOLDER=RESIDUAL ; ! Create the line Evaluate_Expression /EXPRESSION=LIST(VECTOR(METRIC::RESIDUAL::STARTX,METRIC::RESIDUAL::STARTY),VECTOR(METRIC::RESIDUAL::ENDX,METRIC::RESIDUAL::ENDY)) /RESULT_NAME=RESULT_LINE /RESULT_TYPE=METRIC /RESULT_FOLDER=RESIDUAL ;
Graph the Data and Regression Line
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:
Now create a second 2D graph at the same location containing the regression line
The resulting report graph should appear as follows:
Linear_Regression_Explicit Meta-Command
Below are the commands for the Linear_Regression_Explicit Meta-Commands. Go to Pipeline Commands:Meta Commands for details on how to use Meta-commands.
! BEGIN_META ! META_CMD_NAME=Linear_Regression_Explicit ! META_PARAM= SIGNALX : string ::yes ! META_PARAM= SIGNALY : string ::yes ! META_PARAM= NUM_POINTS : string ::yes ! META_PARAM= RESULT_NAME : string ::yes ! META_PARAM= RESULT_FOLDER : string ::yes ! END_META !======================================================================== ! This meta-command will calculate the linear regression of data ! that is passed to the meta-command ! ! Note: Regression Equation: y = b + mx ! ! Slope: m = (NΣXY - (ΣX)(ΣY)) / (NΣX^2 - (ΣX)^2) ! ! Intercept: b = (ΣY - m(ΣX)) / N ! ! where : ! ! x and y are the variables. ! m = The slope of the regression line ! b = The intercept point of the regression line and the y axis. ! N = Number of values or elements ! X = array of x-components ! Y = array of y-components ! ΣX = Sum of x ! ΣY = Sum of y ! ΣXY = Sum of xy ! ΣX^2 = Sum of x^2 !========================================================================== !--------------------------------------------------------------------------- ! Create Temporary Variables - TEMPX and TEMPY from SIGNAL::X and SIGNAL::Y !--------------------------------------------------------------------------- Set_Pipeline_Parameter /PARAMETER_NAME=NAME /PARAMETER_VALUE=::RESULT_NAME ; Set_Pipeline_Parameter /PARAMETER_NAME=FOLDER /PARAMETER_VALUE=::RESULT_FOLDER ; ! Create TEMPX Evaluate_Expression /EXPRESSION=::SIGNALX /RESULT_NAME=TEMPX /RESULT_TYPE=DERIVED /RESULT_FOLDER=RESIDUAL ; ! Create TEMPY Evaluate_Expression /EXPRESSION=::SIGNALY /RESULT_NAME=TEMPY /RESULT_TYPE=DERIVED /RESULT_FOLDER=RESIDUAL ; !---------------------------- ! Sum X and Y !---------------------------- ! Sum X Metric_Sum /RESULT_METRIC_NAME=SUMX /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE /RESULT_METRIC_FOLDER=RESIDUAL /SIGNAL_TYPES=DERIVED /SIGNAL_NAMES=TEMPX /SIGNAL_FOLDER=RESIDUAL /SIGNAL_COMPONENTS=X /EVENT_SEQUENCE= /EXCLUDE_EVENTS= /GENERATE_MEAN_AND_STDDEV=FALSE /APPEND_TO_EXISTING_VALUES=FALSE ; ! Sum Y Metric_Sum /RESULT_METRIC_NAME=SUMY /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE /RESULT_METRIC_FOLDER=RESIDUAL /SIGNAL_TYPES=DERIVED /SIGNAL_NAMES=TEMPY /SIGNAL_FOLDER=RESIDUAL /SIGNAL_COMPONENTS=X /EVENT_SEQUENCE= /EXCLUDE_EVENTS= /GENERATE_MEAN_AND_STDDEV=FALSE /APPEND_TO_EXISTING_VALUES=FALSE ; !---------------------- ! Multiply X and Y !---------------------- Evaluate_Expression /EXPRESSION=DERIVED::RESIDUAL::TEMPX*DERIVED::RESIDUAL::TEMPY /RESULT_NAME=XY /RESULT_TYPE=DERIVED /RESULT_FOLDER=RESIDUAL ; !---------------------- ! Sum XY !---------------------- Metric_Sum /RESULT_METRIC_NAME=SUMXY /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE /RESULT_METRIC_FOLDER=RESIDUAL /SIGNAL_TYPES=DERIVED /SIGNAL_NAMES=XY /SIGNAL_FOLDER=RESIDUAL /SIGNAL_COMPONENTS=X /EVENT_SEQUENCE= /EXCLUDE_EVENTS= /GENERATE_MEAN_AND_STDDEV=FALSE /APPEND_TO_EXISTING_VALUES=FALSE ; !--------------- ! Square X !--------------- Evaluate_Expression /EXPRESSION=DERIVED::RESIDUAL::TEMPX*DERIVED::RESIDUAL::TEMPX /RESULT_NAME=XX /RESULT_TYPE=DERIVED /RESULT_FOLDER=RESIDUAL ; !----------------- ! Sum square of X !----------------- Metric_Sum /RESULT_METRIC_NAME=SUMXX /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE /RESULT_METRIC_FOLDER=RESIDUAL /SIGNAL_TYPES=DERIVED /SIGNAL_NAMES=XX /SIGNAL_FOLDER=RESIDUAL /SIGNAL_COMPONENTS=X /EVENT_SEQUENCE= /EXCLUDE_EVENTS= /GENERATE_MEAN_AND_STDDEV=FALSE /APPEND_TO_EXISTING_VALUES=FALSE ; !------------------ ! Calculate slope !------------------ Evaluate_Expression /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_TYPE=METRIC /RESULT_FOLDER=RESIDUAL ; !---------------------- ! Calculate intercept !---------------------- Evaluate_Expression /EXPRESSION=(METRIC::RESIDUAL::SUMY-METRIC::RESIDUAL::SLOPE*METRIC::RESIDUAL::SUMX)/&::NUM_POINTS /RESULT_NAME=INTERCEPT /RESULT_TYPE=METRIC /RESULT_FOLDER=RESIDUAL ; !-------------------------------------------------------------------------- ! create the resulting metric signal that contains the slope and intercept !-------------------------------------------------------------------------- Evaluate_Expression /EXPRESSION=VECTOR(METRIC::RESIDUAL::INTERCEPT,METRIC::RESIDUAL::SLOPE) /RESULT_NAME=::NAME /RESULT_TYPE=METRIC /RESULT_FOLDER=::FOLDER ; !----------------------------------------------------------- ! clean up the temporary signals ! if you want to see the temporary signals for debugging ! comment out this next command !----------------------------------------------------------- Remove_Signals /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_FOLDER=RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL+RESIDUAL ;