Method of Analysis Used in This Report 



Among several methods available for analyzing observational data 

 that involve interrelationships among independent variables, the one 

 chosen here is that of sequential mioltiple linear regression. It in- 

 volves measures of the relationships of a given dependent variable 

 ("effect") in terms of several controlling environmental "causes" (in- 

 dependent variables), by taking the latter one at a time, two at a time, 

 and so on, until all of the environmental processes are included simul- 

 taneously • 



This sort of analysis is commonly called stepwise regression, and 

 it may be conducted with regression techniques or multiple and partial 

 correlation techniques. These methods also permit study of interrelations 

 among the independent variables themselves, and they are useful for eval- 

 uation of data redundancy. 



Redundant variables, that is, variables that in large part restate 

 what some other variable has already measured, are common in early stages 

 of quantification in the observational sciences, especially when physical 

 models are not clearly discernible in the complex of observations. In 

 these cases a method for "sorting out" a set of independent variables in 

 terms of their importance or meaningfulness in controlling the response 

 of some dependent variable, Y, helps to reduce the number of variables 

 in the set to more manageable proportions. 



We shall illustrate the method with a subset of data from a larger 

 example to be treated more fully in a later section of this paper. The 

 problem here is to examine the near shore bottom slope just seaward of the 

 zone of breaking waves, as it responds to several shore process elements. 



The full example includes a dozen independent variables, designated 

 as XI, X2, ..., X12. We select five of these', retaining the same number 

 designations that they have in the larger example, for ease of later com- 

 parsion. As set up, our introductory example includes the following var- 

 iables: 



Bottom Slope In Shoaling-wave Zone Y 



Mean grain size XI 



Wave period X2 



Wave height XU 



Angle of wave approach X9 



Still-water depth at time of 



slope measurement XIO 



