Regression Solver. User Manual. Process Design and Gas Processing Laboratory Illinois Institute of Technology Chicago, IL,

Transcription

1 Regression Solver User Manual Process Design and Gas Processing Laboratory Illinois Institute of Technology Chicago, IL, Copyright All rights reserved.

2 Introduction Regression Solver is a tool to fit data to a regression model. It is capable of performing linear as well as non-linear regressions. It was developed in MATLAB 2012a. Example A sample data set is provided in Table 1.0 below. Steam To Carbon Molar Ratio Pressure (psia) Temperature (F) Oxygen to Carbon Molar Ratio CH4 (mole fraction in the product gas) Table 1.0 Steam to Carbon Molar ratio, Pressure, Temperature and Oxygen to Carbon Molar ratio are the independent variables. Mole fraction of CH4 in the product gas is a dependent variable.

3 Linear Regression We would like to perform a linear regression to fit the data to the following model: 1. First we need to create a data file in MS-Excel. Here is a snap-shot of the data sheet:

4 Very Important: a. The data should always be in the very first sheet - as in Sheet 1. The sheet can be renamed but it should not be moved around. b. Column headings are very important because they will be used to define the model equation. For e.g.: In this case the model equation is: If we were to label the column headings as: x1, x2, x3, x4 and y, the corresponding equation will be: Save the file in a desired location. This file is saved as CH4_data.xlsx.

5 2. Start the Regression Solver. Here is a snap-shot of the solver: 3. Click the Open button in the INPUT section on the left. Select the file that was just created ( CH4_data.xlsx ) which contains the data. 4. In the Model (Equation) field, specify the equation. In this case it will be: Very Important: a. The ~ must be there which is a representative of is approximately equal to. b. The equation must be correct syntax wise.

6 5. In the equation there are 5 coefficients that need to be solved for. They are a1, a2, a3, a4 and a5. So, we have to provide 5 initial guesses for these coefficients. We can supply the initial guesses randomly and hope for the solution to converge. They need to given as a vector of values. For e.g.: [ ] Here is how to do it: a. Start with the square brackets: [] b. Start filling in the numbers inside the square brackets and press space bar after each number. 6. Finally, click on the Compute button. Wait a while for the solver to figure out everything.

7 7. Here is a screen shot of what we have just done: As we can see all the coefficients have been calculated. Additional statistical information is also displayed which gives insight about how good the model is. 8. This run can be saved by clicking on the Save Data button. The following message box appears:

8 9. All the information about how the save feature works is clearly described in the message box above. In this case, we will name the sheet as Linear Model and click on OK. 10. If we open the data file ( CH4_data.xlsx ), we can see that a new sheet named Linear Model has been created and it contains all the information about the model and extra statistical information.

9 11. There are also three plot tools available to visually interpret the data. They are Residual Histogram, Leverage Plot and Prediction Slice Plots.

10 Non-Linear Regression Let s try to fit the data to a different model equation. Here is the equation: 1. We are using the same data file. 2. Model (Equation) field is changed to: CH4~a1*P^a2 3. Since we only have two coefficients to comptue a1 and a2: Initial values field is changed to: [1 0.1] 4. Finally click on Compute to get the result:

11 5. Save the data by clicking on the Save Data button. Rename the sheet to Power of P Here is the screen shot of the saved file.

12 Very Important: a. Please close the data file before saving any results. It is important to understand that MATLAB won t be able to write anything to an open excel file. If you try to save the run while the original data file is open, the message box won t close and no results will be saved. If this happens, just close the data file and save the run again. b. If there is any sort of error in the process of providing inputs, the OUTPUT side of the solver will display: There is an ERROR. Few Error Types: i. Selecting a wrong data file. ii. Specifying an equation that is not correct syntax wise. P.S.: We are constantly working on improving the software. In the future releases, there will be more features that will provide a more user-friendly experience by guiding the user and displaying messages whenever necessary. If you have any questions please contact: Javad Abbasian Associate Professor of Chemical Engineering Department of Chemical and Biological Engineering Phone: abbasian@iit.edu