I have a question regarding polynomial regression interpretation. In the quadratic model below, all coefficients are significant. But, in the cubic model, the linear and squared coefficients are not significant but the cubic coefficient is significant. The cubic model is a slightly better fit than the quadratic, but not sure if the cubic model should be used given the significance issues. I would greatly appreciate any thoughts on this matter. Thanks!
FYI: day2 = day*day; day3=day*day*day.
*Quadratic model*;
ods graphics on;
proc reg data=no2019; by year;
model sps = day day2 / lackfit;
output out=b
student=sresid
stdp=stderr
p=yhat
r=yresid;
run;
ods graphics off;
The REG Procedure
Model: MODEL1
Dependent Variable: SPS
YEAR=17
Number of Observations Read | 450 |
Number of Observations Used | 450 |
Analysis of Variance | |||||
Source | DF | Sum of | Mean | F Value | Pr > F |
Model | 2 | 1375.32618 | 687.66309 | 192.34 | <.0001 |
Error | 447 | 1598.17313 | 3.57533 |
|
|
Lack of Fit | 2 | 17.24169 | 8.62084 | 2.43 | 0.0895 |
Pure Error | 445 | 1580.93144 | 3.55265 |
|
|
Corrected Total | 449 | 2973.49931 |
|
|
|
Root MSE | 1.89085 | R-Square | 0.4625 |
Dependent Mean | 4.85756 | Adj R-Sq | 0.4601 |
Coeff Var | 38.92605 |
|
|
Parameter Estimates | |||||
Variable | DF | Parameter | Standard | t Value | Pr > |t| |
Intercept | 1 | 7.56219 | 0.20706 | 36.52 | <.0001 |
DAY | 1 | -0.27141 | 0.04139 | -6.56 | <.0001 |
day2 | 1 | 0.00320 | 0.00149 | 2.15 | 0.0321 |
The REG Procedure
Model: MODEL1
Dependent Variable: SPS
YEAR=17
*cubic model*;
ods graphics on;
proc reg data=no2019; by year;
model sps = day day2 day3 / lackfit;
output out=b
student=sresid
stdp=stderr
p=yhat
r=yresid;
run;
ods graphics off;
The REG Procedure
Model: MODEL1
Dependent Variable: SPS
YEAR=17
Number of Observations Read | 450 |
Number of Observations Used | 450 |
Analysis of Variance | |||||
Source | DF | Sum of | Mean | F Value | Pr > F |
Model | 3 | 1391.51323 | 463.83774 | 130.77 | <.0001 |
Error | 446 | 1581.98608 | 3.54705 |
|
|
Lack of Fit | 1 | 1.05463 | 1.05463 | 0.30 | 0.5861 |
Pure Error | 445 | 1580.93144 | 3.55265 |
|
|
Corrected Total | 449 | 2973.49931 |
|
|
|
Root MSE | 1.88336 | R-Square | 0.4680 |
Dependent Mean | 4.85756 | Adj R-Sq | 0.4644 |
Coeff Var | 38.77181 |
|
|
Parameter Estimates | |||||
Variable | DF | Parameter | Standard | t Value | Pr > |t| |
Intercept | 1 | 7.22585 | 0.25946 | 27.85 | <.0001 |
DAY | 1 | -0.07735 | 0.09976 | -0.78 | 0.4385 |
day2 | 1 | -0.01591 | 0.00907 | -1.75 | 0.0800 |
day3 | 1 | 0.00047628 | 0.00022295 | 2.14 | 0.0332 |
The REG Procedure
Model: MODEL1
Dependent Variable: SPS
YEAR=17
Hi,
The purpose is to fit a curve that can be used to estimate or determine when 50% of the maximum average was reached. Here is a graph using the quadratic model.
Thank you, Kyle! That makes good sense.
Mark
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