# Minitab Help 12: Multicollinearity

Minitab Help 12: Multicollinearity##
Minitab^{®}

## 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 x
_{1}. - Perform a linear regression analysis of y vs x
_{2}. - Perform a linear regression analysis of y vs x
_{1}+ x_{2}. - Perform a linear regression analysis of y vs x
_{2}+ x_{1}. - 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-R
^{2}) 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.