# Fitting a Surface By Least Squares in MINITABTM

## Chapter 4, Printout 4

### Section 1: Obtaining the Fit Equation and Numerical Summaries

1. Launch MINITAB.

2. Enter the data.

• Name Column C1 by clicking the column header below the label "C1" and typing, "x1." Then enter the Air Flow data from the "x1i" column in Table 4.8 (p. 150).

• Name Column C2 "x2" and enter the Cooling Water Inlet Temperature data from the "x2i" column in the table.

• Name Column C3 "x3" and enter the Acid Concentration data from the "x3i" column in the table.

• Name Column C4 "y" and enter the Stack Loss data from the "yi" column in the table.

Screenshot:

3. Compute the multiple linear regression.

• Select "Stat --> Regression --> Regression."

• Fill out the resulting dialog box as follows:

Input Type Label Value
Response: y
Predictors: x1 x2 x3

Screenshot:

• Before closing the dialog box, click "Results."

• In the dialog box that follows, click the radio button next to the label, "In addition, the full table of fits and residuals."

Screenshot:

• Click "OK" to close the "Results" dialog box.

• Click "OK" in the "Regression" dialog box.

MINITAB displays summary information, including the regression equation and a table of fits and residuals.

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### Section 2: Generating Additional Plots

1. Display a normal plot of residuals, residuals vs. fits, and residuals vs. x1, x2, and x3.

• Select "Stat --> Regression --> Regression."

• Fill out the resulting dialog box as described in Section 1.

• Before closing the dialog box, click "Graphs."

• Fill out the resulting dialog box as follows:

Input Type Label Value
Regular selected
Histogram of residuals unchecked
Normal plot of residuals checked
Residuals versus fits checked
Residuals versus order unchecked
Residuals versus the variables: x1 x2 x3

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• Click "OK" to close the "Graphs" dialog box.

• Click "OK" in the "Regression" dialog box.

MINITAB displays a normal plot of residuals, a plot of residuals vs. fits, and plots of residuals vs. x1, x2, and x3.

Screenshot (normal plot of residuals):

Screenshot (residuals vs. fits):

Screenshot (residuals vs. x1):

Screenshot (residuals vs. x2):

Screenshot (residuals vs. x3):