yx 



SYMBOLS AND DEFINITIONS 



The F-value may be produced by a multiple regression program and 

 is analogous to the t-value in simple regression (one independent varia- 

 ble) . The F-value indicates the "significance" of r^ and is useful 

 in selecting the most important independent variables. 



^ _ E(y - y): 



r — 



{'-^)'rhti^) 



E(y - y)2 



H]-, height of breaking waves 



n size of the sample 



p total number of independent variables. Caution, several observed car- 

 riers may end up combined into a single independent variable", e.g., 

 X = (gH^,)^/^ sin 2a^ has two distinct carriers (H^ and %) but is 

 one independent variable (see example problem 1). The value of p will 

 be one less than the number of constants to be estimated in Model I, 

 and is equal to the number of constants in Model II. 



r sample correlation coefficient. The r-value produced by regression 



partially measures the closeness of fit between the linear predictor and 

 data. Its square is called the coefficient of determination. 



r2 = 



Z(y - y)^ ^ i:(y - y) (x - x) 



Z(y - y)2 A{y - y)2 Z(x - x) 2 



(Model I) 



Eyx 



(Zy)2(Ex)2 



(Model II) 



SSjj sum of squares of x may be produced by the regression program 

 and is useful for computing other values, e.g., Sg . 



SSx = 5:(x - x)2 

 Sp standard error of the estimated slope, 



fsl 



The larger Sg, the less reliable is the estimate of slope, 

 unbiased estimator of the variance of the random component e, e.j 



„9 2(y - y)^ 



y.x n - p - 1 



in Model I 



The number of independent variables, p, is 1 in simple regression 

 with Model I. The mean square deviation from regression corresponds to 



