# Minitab Help 5: Multiple Linear Regression

Minitab Help 5: Multiple Linear Regression

## Minitab®

### Soapsuds example (using matrices)

• Perform a linear regression analysis of suds on soap.
• Click "Storage" in the regression dialog and check "Design matrix" to store the design matrix, X.
• To create $$X^T$$: Select Calc > Matrices > Transpose, select "XMAT" to go in the "Transpose from" box, and type "M2" in the "Store result in" box.
• To calculate $$X^{T} X$$: Select Calc > Matrices > Arithmetic, click "Multiply," select "M2" to go in the left-hand box, select "XMAT" to go in the right-hand box, and type "M3" in the "Store result in" box. Display the result by selecting Data > Display Data.
• To calculate $$X^{T} Y$$: Select Calc > Matrices > Arithmetic, click "Multiply," select "M2" to go in the left-hand box, select "suds" to go in the right-hand box, and type "M4" in the "Store result in" box. Display the result by selecting Data > Display Data.
• To calculate $$\left(X^{T}X\right)^{-1} \colon$$ Select Calc > Matrices > Invert, select "M3" to go in the "Invert from" box, and type "M5" in the "Store result in" box. Display the result by selecting Data > Display Data.
• To calculate b = $$\left(X^{T}X\right)^{-1} X^{T} Y \colon$$ Select Calc > Matrices > Arithmetic, click "Multiply," select "M5" to go in the left-hand box, select "M4" to go in the right-hand box, and type "M6" in the "Store result in" box. Display the result by selecting Data > Display Data.

### Pastry sweetness

• Obtain a sample correlation
• Create a basic scatterplot.
• Perform a linear regression analysis of Rating on Moisture and Sweetness.
• Click "Storage" in the regression dialog and check "Fits" to store the fitted (predicted) values.
• To create a scatterplot of the data with points marked by Sweetness and two lines representing the fitted regression equation for each group:
• Select Calc > Calculator, type "FITS_2" in the "Store result in variable" box, and type "IF('Sweetness'=2,'FITS')" in the "Expression" box. Repeat for FITS_4 (Sweetness=4).
• Create a basic scatter plot but select "With Groups" instead of "Simple." Select Rating as the "Y variable," Moisture as the "X variable," and Sweetness as the "Categorical variable for grouping."
• Select Editor > Add > Calculated Line and select "FITS_2" to go in the "Y column" and "Moisture" to go in the "X column." Repeat for FITS_4 (Sweetness=4).
• Perform a linear regression analysis of Rating on Moisture.
• Perform a linear regression analysis of Rating on Sweetness.

### Physiological measurements (using matrices)

• Perform a linear regression analysis of BodyFat on Triceps, Thigh, and Midarm.
• Click "Storage" in the regression dialog and check "Design matrix" to store the design matrix, X.
• To create $$X^T$$: Select Calc > Matrices > Transpose, select "XMAT" to go in the "Transpose from" box, and type "M2" in the "Store result in" box.
• To calculate $$X^{T} X$$: Select Calc > Matrices > Arithmetic, click "Multiply," select "M2" to go in the left-hand box, select "XMAT" to go in the right-hand box, and type "M3" in the "Store result in" box. Display the result by selecting Data > Display Data.
• To calculate $$\left(X^{T}X\right)^{-1} \colon$$ Select Calc > Matrices > Invert, select "M3" to go in the "Invert from" box, and type "M4" in the "Store result in" box. Display the result by selecting Data > Display Data.

### Measurements of college students

 [1] Link ↥ Has Tooltip/Popover Toggleable Visibility