c. The Model Building Process . There were 47 independent variables 

 in the original model. Silt was omitted since the percent sand, silt 

 and clay always sums to 100 percent. This causes any two of these varia- 

 bles to correlate perfectly with the third; therefore, only two of the 

 variables can be used in a regression equation. The number of variables 

 in the original model was reduced with the stepwise regression procedure 

 and the maximum R 2 improvement procedure. By regression techniques, 

 two sets of variables most likely to be related to yield (Tab. 29) and 

 height (Tab. 30) were selected. Each model contains 11 variables with an 

 R 2 of 0.90. Thus, about 90 percent of the variation in yield and height 

 is explained by the independent variables in each regression equation. 

 The variables in these models represent a subset of variables which can 

 be used to explain differences in yield and height; however, they may not 

 be the most important variables affecting plant growth in the salt marsh 

 system. Other subsets may produce similar R 2 values, but the two pre- 

 sented were considered the most agronomical ly feasible. Some models with 

 fewer variables also produced satisfactory R 2 values (Tab. 31)= 

 Regression equations with more independent variables produced higher R 2 

 values, but beyond 11 variables there was very little increase in the 

 regression sum of squares or reduction in the error mean square and the 

 coefficient of variation. 



d. Interpretation of the Yield Model . As would be expected in a 

 natural ecological system, an examination of the correlation matrix for 

 the 11 variables in the model revealed that there was some intercorrela- 

 tion of variables. When there is a correlation between independent 

 variables in a model, the regression coefficients (b's) may not ke 

 reliable (Draper and Smith, 1966) . However, by considering the regres- 

 sion model in combination with the simple correlations of each independent 

 variable with yield (Tab. 27) and the means and Least Significant 

 Differences obtained by analysis of variance, some insight as to the effect 

 of each variable on yield variation may be obtained. The partial sum of 

 squares are a measure of the relative importance of the variables in a 

 regression equation and the variables may be ranked on this basis (Tab. 



29) (Draper and Smith, 1966). 



The potassium content of the plant tissue at the fall sampling data 

 (CK) is the variable which accounts for the highest amount of yield 

 variation in the regression equation. At five of the seven locations, 

 potassium concentrations were greater in plants taken from the short 

 height zone (Tab. 32). The trend of lower potassium concentrations in 

 higher yielding plants is probably an indication of a greater dilution of 

 potassium in the plant tissue where higher yields occur. 



Sodium concentration of the plant tissue at the first sampling date 

 (ANa) is positively related to yield. Significant differences in sodium 

 concentrations occur between height zones and locations (Tab. 32). 

 Plants from the tall height zones had higher concentrations than those 

 from the short height zones. The explanation for this is not apparent, 

 particularly since higher salinities of the soil solution (AS-SAL) were 

 clearly related to decreased yields (Tab. 27). High salinity of the soil 



112 



