Finding the ridge constant d: Hoerl and Kennard suggest plotting the entries in b+ d against values of d ranging between 0 and 1. The resulting graph, called a ridge trace, both furnishes a visual...

Finding the ridge constant d: Hoerl and Kennard suggest plotting the entries in b+ d against values of d ranging between 0 and 1. The resulting graph, called a ridge trace, both furnishes a visual representation of the instability due to collinearity and (ostensibly) provides a basis for selecting a value of d. When the data are collinear, we generally observe dramatic changes in regression coefficients as d is gradually increased from 0. As d is increased further, the coefficients eventually stabilize and then are driven slowly toward 0. The estimated error variance, S+2 E , which is minimized at the least-squares solution (d = 0), rises slowly with increasing d. Hoerl and Kennard recommend choosing d so that the regression coefficients are stabilized and the error variance is not unreasonably inflated from its minimum value. (A number of other methods have been suggested for selecting d, but none avoids the fundamental difficulty of ridge regression—that good values of d depend on the unknown β_s.) Construct a ridge trace, including the regression standard error S+ E, for B. Fox’s Canadian women’s labor force participation data. Use this information to select a value of the ridge constant d, and compare the resulting ridge estimates of the regression parameters with the least-squares estimates. Make this comparison for both standardized and unstandardized coefficients. In applying ridge regression to these data, B. Fox selected d = 0:05.