Appendix B. Residual transformation equations and SYSTAT output for backwards stepwise sequential regression. OD = original wave orbital displacement (in meters); W' = wind velocity (in meters/s) after removing variability shared with OD; LTD' = average tidal height (in meters) after removing variability shared with OD, and W'; BD' = wave breaking depth (in meters) after removing variability shared with OD, W', and LTD'. Transformed data were created by applying residual transformation equations (B) to original explanatory variables (same as used in Appendix A). Backwards stepwise multiple regression was then run on the transformed data using MGLH:REGRESSION under the STATS menu in SYSTAT 5.2 for Macintosh. Response was the dependent variable (same as used in Appendix A); CONSTANT, OD, W', LTD', and BD' were the dependent variables; Stepwise was set to custom, with a backwards step order, and P = 0.15 to remove. Only standard SYSTAT output is presented.
|
Transformation
equation 1
|
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| DEP VAR: W N: 38 MULTIPLE R: 0.681; SQUARED MULTIPLE R: 0.464; ADJUSTED SQUARED MULTIPLE R: 0.449; STANDARD ERROR OF ESTIMATE: 6.032 | ||||||
| VARIABLE | COEFF | SE | STD COEF | TOLER | F | P |
| CONST | -15.5166 | 3.297 | 0.00 | N/A | -4.71 | 0.0000 |
| OD | 6.809 | 1.218 | 0.68 | 1.0 | 5.59 | 0.0000 |
|
ANALYSIS
OF VARIANCE
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| SOURCE | SS | DF | MS | F | P | |
| REGRESSION | 1135.46 | 1 | 1135.46 | 31.02 | 0.0000 | |
| RESIDUAL | 1309.77 | 36 | 36.38 | |||
| Equation 1: W' = W + 15.5166 + (-6.8019 * OD) | ||||||
|
Transformation
equation 2
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| LTD regressed against OD and W' using simple linear regression | ||||||
| DEP VAR: LTD N: 38; MULTIPLE R: 0.360; SQUARED MULTIPLE R: 0.130; ADJUSTED SQUARED MULTIPLE R: 0.080; STANDARD ERROR OF ESTIMATE: 0.177 | ||||||
| VARIABLE | COEFF | SE | STD COEF | TOLER | F | P |
| CONST | -14.6982 | 0.094 | 0.00 | N/A | -1.57 | 0.1249 |
| OD | -0.06152 | 0.035 | -0.28 | 1.0 | -1.78 | 0.0835 |
| W' | -0.00676 | 0.008 | -0.23 | 1.0 | -1.43 | 0.1614 |
|
ANALYSIS
OF VARIANCE
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| SOURCE | SS | DF | MS | F | P | |
| REGRESSION | 0.15 | 2 | 0.08 | 2.61 | 0.0877 | |
| RESIDUAL | 1.02 | 35 | 0.03 | |||
| Equation 2: LTD' = LTD + 14.6982 + (0.06152 * OD) + (0.00676 * W') | ||||||
|
Transformation
equation 3
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| BD regressed against OD, W', and LTD' using simple linear regression | ||||||
| DEP VAR: BD N: 38; MULTIPLE R: 0.759; SQUARED MULTIPLE R: 0.575; ADJUSTED SQUARED MULTIPLE R: 0.538; STANDARD ERROR OF ESTIMATE: 1.161 | ||||||
| VARIABLE | COEFF | SE | STD COEF | TOLER | F | P |
| CONST | 0.73579 | 0.634 | 0.00 | N/A | 1.16 | 0.2542 |
| OD | 1.52702 | 0.234 | 0.73 | 1.0 | 6.52 | 0.0000 |
| W' | 0.05388 | 0.032 | 0.19 | 1.0 | 1.68 | 0.1021 |
| LTD' | -1.00787 | 1.147 | -0.09 | 1.0 | -0.88 | 0.3856 |
|
ANALYSIS
OF VARIANCE
|
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| SOURCE | SS | DF | MS | F | P | |
| REGRESSION | 62.07 | 3 | 20.69 | 15.36 | 0.0000 | |
| RESIDUAL | 45.81 | 34 | 1.35 | |||
| Equation 3: BD' = BD – 0.73579 + (-1.52702 * OD) + (-0.05388 * W') + (1.00787 * LTD') | ||||||
|
Backwards
stepwise variable selection
|
| DEPENDENT VARIABLE: RESPONSE |
| MINIMUM TOLERANCE FOR ENTRY INTO MODEL = 0.010000 |
|
Initial model
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| STEP #0; R = 0.775; RSQUARE = 0.601 | ||||||
| IN | ||||||
| --- | ||||||
| VARIABLE | COEFF | SE | STD COEF | TOLER | F | P |
| 1 CONST | ||||||
| 2 OD | 0.1942 | 0.029 | 7.40 | 1.0 | 45.0 | 0.0000 |
| 3 W' | 0.0081 | 0.004 | 0.22 | 1.0 | 4.18 | 0.0489 |
| 4 LTD' | -0.0553 | 0.141 | -0.04 | 1.0 | 0.15 | 0.6980 |
| 5 BD' | 0.0043 | 0.021 | -0.02 | 1.0 | 0.04 | 0.8403 |
| OUT | PART. CORR | |||||
| --- | ||||||
| none | ||||||
|
1st variable
removal
|
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| STEP #1; R = 0.775; RSQUARE = 0.600 | ||||||
| TERM REMOVED: BD' | ||||||
| IN | ||||||
| --- | ||||||
| VARIABLE | COEFF | SE | STD COEF | TOLER | F | P |
| 1 CONST | ||||||
| 2 OD | 0.1942 | 0.0284 | 7.40 | 1.0 | 47.0 | 0.0000 |
| 3 W' | 0.0081 | 0.0039 | 0.22 | 1.0 | 4.30 | 0.0457 |
| 4 LTD' | -0.0553 | 0.1393 | -0.04 | 1.0 | 0.16 | 0.6938 |
| OUT | PART. CORR | |||||
| --- | ||||||
| 5 BD' | -0.035 | N/A | N/A | 0.42462 | 0.04 | 0.8403 |
|
2nd variable
removal
|
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| STEP #2; R = 0.773; RSQUARE = 0.598 | ||||||
| TERM REMOVED: LTD' | ||||||
| IN | ||||||
| --- | ||||||
| VARIABLE | COEFF | SE | STD COEF | TOLER | F | P |
| 1 CONST | ||||||
| 2 OD | 0.1941 | 0.0284 | 7.40 | 1.0 | 48.0 | 0.0000 |
| 3 W' | 0.0081 | 0.0038 | 0.22 | 1.0 | 4.41 | 0.0431 |
| OUT | PART. CORR | |||||
| --- | ||||||
| 4 LTD' | -0.068 | N/A | N/A | 1.0 | 0.16 | 0.6938 |
| 5 BD' | -0.035 | N/A | N/A | 1.0 | 0.04 | 0.8383 |
| THE SUBSET MODEL INCLUDES THE FOLLOWING PREDICTORS: | ||||||
| CONSTANT | ||||||
| OD | ||||||
| W' | ||||||
|
Parameterization
of final model
|
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| DEP VAR: RESPONSE
N: 38; MULTIPLE R: 0.773; SQUARED MULTIPLE R: 0.598; ADJUSTED SQUARED MULTIPLE
R: 0.575; STANDARD ERROR OF ESTIMATE:
0.139 |
||||||
| VARIABLE | COEFF | SE | STD COEF | TOLER | F | P |
| CONST | 2.748 | 0.076 | 0.00 | N/A | 36.0 | 0.0000 |
| OD | 0.194 | 0.028 | 0.74 | 1.0 | 6.91 | 0.0000 |
| W' | 0.008 | 0.004 | 0.22 | 1.0 | 2.09 | 0.0431 |
|
Analysis
of variance
|
|||||
| SOURCE | SS | DF | MS | F | P |
| REGRESSION | 1.012 | 2 | 0.51 | 26.06 | 0.0000 |
| RESIDUAL | 0.679 | 35 | 0.02 | ||