First, for a given outcome, its counterfactual measurements (i.e., those without the policy change) during the postimplementation period and its preimplementation observations formed a curvilinear trend line.
While we adopted highly flexible splines to capture the curvilinear trends, we must acknowledge that unmeasured variation may have occurred during 2008 that could add noise into our results.
Human PCB determinations presented in Figure 1 show a curvilinear trend. Also, the minimum and maximum PCB concentrations in fish, plotted in Figure 2, show a curvilinear pattern.
We identified two halves of a curvilinear trend: increasing PCB concentrations from the 1990s back to the 1980s and decreasing PCB concentrations from the 1980s back to the 1970s.
A visual inspection of this data plotting strongly reinforces the curvilinear pattern that was concluded previously and demonstrates that the curvilinear trend
line was in fact a reasonable and adequate representation of actual market behavior.
In addition, curvilinear trend
lines will be extended to the turn of the century.
Many examples of that blatant omission are apparent: The chapter on loss forecasting suggests that in making adjustments for price level changes, the risk manager should "round the result to the nearest $100 to simplify later calculations," thus implying that the appropriate use of computer systems for this procedure had been overlooked; and a later statement in this chapter suggests that a risk manager should "turn to a trained statistician" because computing a curvilinear trend
line is complex--although, again, one could expect a present-day risk manager to use an appropriate software package for this purpose.
Holistic ratings showed no significant linear or curvilinear trend
over the four assessment periods, partly due to the variability among individual scores.
Trends based on the stronger of three or four years of history diminish linear effects, as do polynomials that establish curvilinear trends
. Build spreadsheets that provide options of the strongest trend (linear or curvilinear, based on varied years of history).
So will using a polynomial trending that will seek out curvilinear trends
. Build spreadsheets that provide options of the strongest trend (linear or curvilinear based on varied years of history).
The current paper demonstrates that when multicollinearity exists and the true model does not include curvilinear trends
, adding quadratic terms does increase the probability of type II error in detecting interaction.
The 11 averages (1 average/yr) for each treatment in each field were analyzed to determine whether there were linear or curvilinear trends
between average PS and time.