[OriginPro] Plot from a Formula: Useful for Multiple Linear Regression or Simple Linear Regression

Background

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After completing a multiple linear regression analysis, presenting the results only as a formula can feel too abstract and monotonous. This article uses OriginPro to walk through three methods for visualizing functions, with a special demonstration of how to combine scatter plots and function plots.

Basic Visualization Methods

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Method 1: Quick Function-Plot Drawing

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1. Operation path: Click the top menu Plot > Function Plot > 2D Function Plot.
2. Formula input rules:
   • Merge all independent variables into a single symbol x. If there are multiple independent variables, enter all of them as x; do not enter x1, x2, and so on because of software syntax limits.
   • Example: the original formula y=0.217x₁+0.115x₂+0.416x₃+0.24x₄ should be rewritten as y=0.217*x+0.115*x+0.416*x+0.24*x.
3. Parameter suggestions:
   • Points refer to the number of plotted points. From previous knowledge, we know points can form a line. The more points there are, the smoother the line becomes.
   • From and To represent the value range of x.
   • Here we are drawing a straight line, so set the number of points to 100 and the x range from 0 to 10. If you want to draw a curve, you can increase the number of points appropriately.

     

4. Graph optimization: After clicking OK, the graph is created. Finally, beautify it as needed.

   

Method 2: Set Column Values

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1. Set the independent variable:

   • First left-click A(X), then right-click and choose Set Column Values, and enter the range and formula.
   • Note that Row should be set to i, not x.
   • From(F) and To(T) define the value range of the independent variable i. In testing, the minimum F value can only be set to 0, representing the number of points.
   • Col sets the specific values of the independent variable. It is best to use n*i, which generates an arithmetic sequence.

   

2. Set the dependent variable:

   • Left-click B(Y), then right-click and choose Set Column Values, and enter the range and formula.
   • Here, Row can be set to automatic. The system will automatically match the number of dependent-variable values according to the independent-variable range.
   • Enter the formula directly in Col. Note that because we set the independent variable in column A, x should be entered as A here.

   

3. Generate the chart: Select all the data and draw a line chart.

Method 3: Quick Formula-Cell Method

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• Directly double-click the F(x) cell below the table and enter the formula. The requirements are the same as in Method 2.

• Feature: It generates results quickly, but the default number of points is small. If you need to adjust it manually, right-click the column and open Column Properties.

  

Advanced Application: Overlaying a Scatter Plot and Function Plot

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Scatter + function plots are more commonly used in simple linear regression, but if you want to draw a similar chart for multiple regression, that is also possible.

1. Export function data: Note: if you already have function data from Method 2 or Method 3, you do not need this step. This step is only for a little convenience.

   • In Method 1, after drawing the function plot, double-click the chart, click Function, and change the function settings. Then click Workbook to export the function data into a table.

     

2. Preprocess the data:

   • Paste the exported data, meaning the data used for linear regression analysis, into an OriginPro worksheet. At this point, set the independent variable as Y and the dependent variable as X to make plotting easier.

     

3. Create the base scatter plot:

   • Select all data > Plot > Basic 2D > Scatter.
   • Click the far-right Swap XY button to align the coordinate direction.

   

4. Add the function graph:

   • Right-click a blank area and choose New Layer (Axes) > No Axes (linked dimensions/scale to XY axes)(N).
   • In the chart window, select “2,” then right-click Plot Setup.

   

5. Adjust:

   • First choose Line, then select the table containing the function data in the upper window, set the X and Y axes, and click “Apply” to confirm.
   • If you do not want the coordinate axes to change, uncheck “Rescale.”
   • If the worksheet is not displayed, click the far-right arrow beside Show(S) to display the workbook.

     

6. After that, the chart is finished. You can then beautify and adjust it as needed.

   

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