# Inference for Multiple Linear Regression in JMP®

## Chapter 9, Printout 2

1. Launch JMP and create a new data table.

2. Enter the data.

• Rename Column 1 to "x1" and enter the Air Flow data from the x1i column in Table 4.8 (p. 150).

• Add a second column, "x2," and enter the Cooling Water Inlet Temperature data from the x2i column in the table.

• Add a third column, "x1^2"

• Double-click the column header, "x1^2."

• In the dialog box that follows, select "New Property --> Formula."

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• Click "Edit Formula."

• In the dialog box that follows, double-click on the words, "no formula." Enter ":x1^2"

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Note: When you finish editing the function, JMP will display it in a graphically-editable form. Functions can also be entered graphically using the "Table Columns" list and the arithmetic buttons. This approach is more intuitive, though more time-consuming.

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

• Click "OK" in the column properties dialog box.

JMP fills the "x1^2" column with the squares of the values in "x1."

• Add a fourth column, "y," and enter the Stack Loss data from the yi column in Table 4.8.

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3. Compute the multiple linear regression.

• Select "Analyze --> Fit Model."

• In the "Select Columns" list in the dialog box that follows, click "y"; then click the "Y" button to designate y as the response variable.

• Click "x1" in the "Select Columns" list and click "Add" to designate x1 as a factor variable. Do the same for x2 and x1^2.

• Select "Standard Least Squares" from the pop-up menu labeled "Personality" if it is not already selected. (This should be the default.)

• Select "Minimal Report" from the pop-up menu labeled "Emphasis."

• Leave the checkbox labeled "No Intercept" unchecked.

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• Click "Run Model."

JMP computes a fit and displays summary information.

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4. Display confidence limits for parameters.

• Right-click anywhere on the table under the label "Parameter Estimates."

• Select "Columns --> Lower 95%" from the resulting pop-up menu.

• Right-click on the table again, this time selecting "Columns --> Upper 95%" from the pop-up menu.

JMP adds two columns to the Parameter Estimates table.

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5. Generate a predicted value for x1 = 60, x2 = 20

• Click the red triangle next to the label, "Response y." Select "Save Columns --> Prediction Formula" from the resulting pop-up menu.

• Again, click the red triangle next to the label, "Response y." Select "Save Columns --> StdErr Pred Formula" from the resulting pop-up menu.

JMP saves the formulas to new columns in the data table.

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• Add a new data point to the table by entering 60 in row 18 of the "x1" column and 20 to row 18 of the "x2" column.

JMP computes a value for x1^2, a predicted y, and a standard error for the prediction.

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