# Minitab Help 5: MLR Model & Evaluation

### IQ and physical characteristics

- Create a simple matrix of scatter plots.
- Perform a linear regression analysis of PIQ on Brain, Height, and Weight.
- Click "Options" in the regression dialog to choose between Sequential (Type I) sums of squares and Adjusted (Type III) sums of squares in the Anova table.

### Underground air quality

- Create a simple matrix of scatter plots.
- Select Graph > 3D Scatterplot (Simple) to create a 3D scatterplot of the data.
- Perform a linear regression analysis of Vent on O2 and CO2.
- Click "Options" in the regression dialog to choose between Sequential (Type I) sums of squares and Adjusted (Type III) sums of squares in the Anova table.

### 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 (X
^{T}X)^{-1}: 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 = (X
^{T}X)^{-1}X^{T}Y: 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.

### Heart attacks in rabbits

- Perform a linear regression analysis of Infarc on Area, X2 (early cooling), and X3 (late cooling).
- 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 group and three lines representing the fitted regression equation for each group:
- Select Calc > Calculator, type "FITS_1" in the "Store result in variable" box, and type "IF('Group'=1,'FITS')" in the "Expression" box. Repeat for FITS_2 (Group 2) and FITS_3 (Group 3).
- Create a basic scatter plot but select "With Groups" instead of "Simple." Select Infarc as the "Y variable," Area as the "X variable," and Group as the "Categorical variable for grouping."
- Select Editor > Add > Calculated Line and select "FITS_1" to go in the "Y column" and "Area" to go in the "X column." Repeat for FITS_2 (Group 2) and FITS_3 (Group 3).

### Student heights and GPAs

- Perform a linear regression analysis of gpa on height.
- Create a fitted line plot to create a scatterplot of the data with a fitted simple linear regression line. Select Editor > Add > Reference Lines to add a horizontal line at the mean of gpa.
- SSE for the full model is in the SSE row of the Anova table.
- SSE for the reduced model is in the Total row of the Anova table.
- The overall F statistic and p-value are in the Regression row of the Anova table.

### Skin cancer mortality

- Perform a linear regression analysis of Mort on Lat.
- Create a fitted line plot to create a scatterplot of the data with a fitted simple linear regression line. Select Editor > Add > Reference Lines to add a horizontal line at the mean of Mort.
- SSE for the full model is in the SSE row of the Anova table.
- SSE for the reduced model is in the Total row of the Anova table.
- The overall F statistic and p-value are in the Regression row of the Anova table.

### Alcoholism and muscle strength

- Perform a linear regression analysis of strength on alcohol.
- SSE for the full model is in the SSE row of the Anova table.
- SSE for the reduced model is in the Total row of the Anova table.
- The overall F statistic and p-value are in the Regression row of the Anova table.

### Allen cognitive level study

- Perform a linear regression analysis of ACL on:
- Vocab (with default adjusted sums of squares).
- Vocab and SDMT (with adjusted sums of squares).
- Vocab and SDMT (click "Options" to switch to sequential sums of squares).
- SDMT (click "Options" to switch back to adjusted sums of squares).
- SDMT and Vocab (with adjusted sums of squares).
- SDMT and Vocab (click "Options" to switch to sequential sums of squares).
- SDMT, Vocab, and Abstract (with sequential sums of squares).

### Heart attacks in rabbits (revisited)

- Perform a linear regression analysis of Infarc on:
- Area, X2, and X3 (with default adjusted sums of squares).
- Area.
- Area, X2, and X3 (click "Options" to switch to sequential sums of squares).

- Find an F-based P-value.

### Pastry sweetness

- Create a correlation matrix.
- 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.

### Female stat students

- Create a simple matrix of scatter plots.
- Perform a linear regression analysis of Height on momheight and dadheight.
- Create residual plots and select "Residuals versus fits" (with regular residuals).

### Hospital infections

- Perform a linear regression analysis of InfctRsk on Stay, Age, and Xray.

### 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 (X
^{T}X)^{-1}: 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.

### Peruvian blood pressure

- Use Calc > Calculator to calculate FracLife variable.
- Perform a linear regression analysis of Systol on nine predictors.
- Perform a linear regression analysis of Systol on four predictors.
- Find an F-based P-value.

### Measurements of college students

- Perform a linear regression analysis of Height on LeftArm, LeftFoot, HeadCirc, and nose.
- Create residual plots and select "Residuals versus fits" (with regular residuals).
- Perform a linear regression analysis of Height on LeftArm and LeftFoot.
- Find an F-based P-value.
- Perform a linear regression analysis of Height on LeftFoot.