Multicollinearity

EXAMPLE: Sediment Yield in Mountain Basins

We have data for 19 mountain basis mostly in the Southern Alps of New Zealand (Hicks, McSavenay, and Chinn, 1990). The authors found that sediment yield was determined largely by runoff and precipitation. To linearize relationships we'll take log base 10 of all variables. (as suggested by the authors) see page 139 RWG

Variables:

• Mean Annual Stream Sediment yield (tons/km^2)
• Mean Annual Runoff (mm)
• Mean Annual precipitation (mm)

Plots/output:

1. Simple Linear Regression log(sediment) on log(runoff)
2. Simple Linear Regression log(sediment) on log(precipitation)
3. Multiple Regression log(sediment) on log(precipitation) and log(runoff)
4. Added Variable Plots
5. Scatter Plot Matrix and Correlation matrix
6. Case Statistics and False Discovery Rate Procedure

Identifying Multicollinearity:

1. Scatterplot and correlation matrices of the variables
2. Correlation matrix of parameter estimates
3. Tolerance