Minitab Help 12: Multicollinearity

Blood pressure (multicollinearity)

• Create a simple matrix of scatterplots of the data.
• Obtain a sample correlation between the variables.

Uncorrelated predictors (no multicollinearity)

• Create a simple matrix of scatterplots of the data.
• Obtain a sample correlation between the predictors.
• Perform a linear regression analysis of y vs x₁.
• Perform a linear regression analysis of y vs x₂.
• Perform a linear regression analysis of y vs x₁ + x₂.
• Perform a linear regression analysis of y vs x₂ + x₁.
• Select Graph > 3D Scatterplot to create a 3D scatterplot of the data.

Blood pressure (predictors with almost no multicollinearity)

• Create a simple matrix of scatterplots of the data.
• Perform a linear regression analysis of BP vs Stress.
• Perform a linear regression analysis of BP vs BSA.
• Perform a linear regression analysis of BP vs Stress + BSA.
• Perform a linear regression analysis of BP vs BSA + Stress.
• Select Graph > 3D Scatterplot to create a 3D scatterplot of the data.

Blood pressure (predictors with high multicollinearity)

• Create a simple matrix of scatterplots of the data.
• Perform a linear regression analysis of BP vs Weight.
• Perform a linear regression analysis of BP vs BSA.
• Perform a linear regression analysis of BP vs Weight + BSA.
• Perform a linear regression analysis of BP vs BSA + Weight.
• Select Graph > 3D Scatterplot to create a 3D scatterplot of the data.
• Find a confidence interval and a prediction interval for the response to predict BP for Weight=92 and BSA=2 for the two simple linear regression models and the multiple linear regression model.

Poverty and teen birth rate (high multicollinearity)

• Select Data > Subset Worksheet to create a worksheet that excludes the District of Columbia.
• Create a simple matrix of scatterplots of the data.
• Perform a linear regression analysis of PovPct vs Brth15to17.
• Perform a linear regression analysis of PovPct vs Brth18to19.
• Perform a linear regression analysis of PovPct vs Brth15to17 + Brth18to19.

Blood pressure (high multicollinearity)

• Perform a linear regression analysis of BP vs Age + Weight + BSA + Dur + Pulse + Stress.
• Perform a linear regression analysis of Weight vs Age + BSA + Dur + Pulse + Stress and confirm the VIF value for Weight as 1/(1-R²) for this model.
• Perform a linear regression analysis of BP vs Age + Weight + Dur + Stress.

Allen Cognitive Level study (reducing data-based multicollinearity)

• Create a simple matrix of scatterplots of the sampled allentestn23 data.
• Obtain a sample correlation between Vocab and Abstract.
• Perform a linear regression analysis of ACL vs SDMT + Vocab + Abstract.
• Repeat for the full allentest data.

Exercise and immunity (reducing structural multicollinearity)

• Create a basic scatterplot of igg vs oxygen.
• Select Calc > Calculator to calculate an oxygen-squared variable named oxygensq.
• Perform a linear regression analysis of igg vs oxygen + oxygensq.
• Create a fitted line plot and select "Quadratic" for the type of regression model.
• Create a basic scatterplot of oxygensq vs oxygen.
• Obtain a sample correlation between oxygensq and oxygen.
• Select Calc > Calculator to calculate a centered oxygen variable named oxcent and an oxcent-squared variable named oxcentsq.
• Perform a linear regression analysis of igg vs oxcent + oxcentsq.
• Create a fitted line plot and select "Quadratic" for the type of regression model.
• Perform a linear regression analysis of igg vs oxcent.
• Create residual plots to create a residual vs fits plot and a normal probability plot for the centered quadratic model.
• Find a confidence interval and a prediction interval for the response to predict igg for oxygen = 70 using the centered quadratic model.