Polynomial regression for Ricker data

Obs n logR nbar x x2 x3
1 5 0.42 50.455 -45.455 2066.16 -93917.17
2 10 0.33 50.455 -40.455 1636.61 -66208.94
3 20 0.48 50.455 -30.455 927.51 -28247.23
4 30 0.03 50.455 -20.455 418.41 -8558.52
5 40 -0.18 50.455 -10.455 109.31 -1142.80
6 50 -0.16 50.455 -0.455 0.21 -0.09
7 60 0.08 50.455 9.545 91.11 869.62
8 70 -1.20 50.455 19.545 382.01 7466.33
9 80 -1.45 50.455 29.545 872.91 25790.04
10 90 -1.72 50.455 39.545 1563.81 61840.75
11 100 -2.67 50.455 49.545 2454.71 121618.46
Polynomial regression for Ricker data; Plot of logR by n logR -3 -2 -1 0 1 n 0 10 20 30 40 50 60 70 80 90 100 Polynomial regression for Ricker data

Polynomial regression for Ricker data

The GLM Procedure

Number of Observations Read 11
Number of Observations Used 11

Polynomial regression for Ricker data

The GLM Procedure

 

Dependent Variable: logR

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 10.30624576 3.43541525 40.89 <.0001
Error 7 0.58804515 0.08400645    
Corrected Total 10 10.89429091      
R-Square Coeff Var Root MSE logR Mean
0.946023 -52.78519 0.289839 -0.549091
Source DF Type I SS Mean Square F Value Pr > F
x 1 9.22443700 9.22443700 109.81 <.0001
x2 1 1.04566094 1.04566094 12.45 0.0096
x3 1 0.03614783 0.03614783 0.43 0.5328
Source DF Type III SS Mean Square F Value Pr > F
x 1 0.84098563 0.84098563 10.01 0.0158
x2 1 0.92650412 0.92650412 11.03 0.0127
x3 1 0.03614783 0.03614783 0.43 0.5328
Parameter Estimate Standard
Error		 t Value Pr > |t|
Intercept -.1955039898 0.13558587 -1.44 0.1925
x -.0242363062 0.00765999 -3.16 0.0158
x2 -.0003643651 0.00010972 -3.32 0.0127
x3 -.0000028427 0.00000433 -0.66 0.5328
Polynomial regression for Ricker data; Plot of logR by n logR -3 -2 -1 0 1 n 0 10 20 30 40 50 60 70 80 90 100 Polynomial regression for Ricker data

Polynomial regression for Ricker data

The REG Procedure

Model: MODEL1

Dependent Variable: logR

Number of Observations Read 11
Number of Observations Used 11
Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 10.27010 5.13505 65.81 <.0001
Error 8 0.62419 0.07802    
Corrected Total 10 10.89429      
Root MSE 0.27933 R-Square 0.9427
Dependent Mean -0.54909 Adj R-Sq 0.9284
Coeff Var -50.87099    
Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t| Standardized
Estimate		 Tolerance Variance
Inflation		 95% Confidence Limits
Intercept 1 -0.18655 0.13000 -1.43 0.1892 0 . 0 -0.48634 0.11324
x 1 -0.02890 0.00273 -10.59 <.0001 -0.89833 0.99505 1.00497 -0.03520 -0.02261
x2 1 -0.00037900 0.00010353 -3.66 0.0064 -0.31058 0.99505 1.00497 -0.00061774 -0.00014026

Polynomial regression for Ricker data

The REG Procedure

Model: MODEL1

Dependent Variable: logR

Polynomial regression for Ricker data; Panel of fit diagnostics for logR. Fit Diagnostics for logR 0.9284 Adj R-Square 0.9427 R-Square 0.078 MSE 8 Error DF 3 Parameters 11 Observations Proportion Less 0 1 Residual 0 1 Fit–Mean -2 -1 0 1 -0.75 0 0.75 Residual 0 10 20 30 40 Percent 2 4 6 8 10 Observation 0.0 0.2 0.4 Cook's D -2 -1 0 Predicted Value -2 -1 0 logR -1 0 1 Quantile -0.4 0.0 0.4 Residual 0.2 0.4 0.6 Leverage -2 0 2 4 RStudent -2 -1 0 Predicted Value -2 0 2 4 RStudent -2 -1 0 Predicted Value -0.2 0.2 0.6 Residual
Polynomial regression for Ricker data; Panel of scatterplots of residuals by regressors for logR. Residual by Regressors for logR 0 1000 2000 x2 -40 -20 0 20 40 x -0.2 0.0 0.2 0.4 0.6 Residual

Polynomial regression for Ricker data

The REG Procedure

Model: MODEL1

Partial Regression Residual Plot

Polynomial regression for Ricker data; Panel of partial regression scatterplots by regressors for logR. Partial Plots for logR Partial Regressor Residual Partial Dependent Residual -1000 0 1000 -0.5 0.0 0.5 1.0 x2 -40 -20 0 20 40 -1.5 -0.5 0.5 1.5 x -0.5 0.0 0.5 1.0 -0.4 0.0 0.4 Intercept