Part VIII.
Mathematical Modeling of Annual Average Temperature Time
Series From Greenwood, MD
copyright © 2007 Paolo B. DePetrillo, MD
Here is the linear fit, which is much much better than the
mean fit. The best model for a linear fit did not have an
intercept.
T = 0.003 ± 0.001(Year) + 6 ± 4; SSE 46.00 MSE 0.44 RMSE
0.66
Full Model
T = P(1+3i)) x Cosine {(Year+ P(2+3i)) *3.1415) / P(3+3i);
i=0 to 4; + P16 x {Cosine {(Year +P17) *3.1415) / P18}
* (LogSun,lag 0 years + 2*LogSun, lag 1 years + 2*LogSun,
lag 2 years +2*LogSun, lag 3 years+2*LogSun, lag 4 years +
LogSun, lag 5 years )
+ P19
Click here for model parameters
Comparing to
linear fit
Compare models with the corrected Akaike's Information
Criteria
Linear Model Full Model
Sum-of-squares 46.00 26.53
Number of data points 103 103
Number of parameters 2 19
Akaike's Information Criteria (corrected, AICc) -76.78
-89.47
Probability model is correct 0.18% 99.82%
Difference in AICc 12.69
Information ratio 568.54
Full Model has a lower AICc than Linear Model so is more
likely to be the correct model.
It is 568.5 times more likely to be correct than Linear
Model.
Compare models with F test
Model SS DF
Linear Model (null) 46.00 101
Full Model (alternative) 26.53 84
Difference 19.47 17
Percentage Difference 73.39% 20.24%
Ratio (F) 3.63
P value <0.0001
If Linear Model (the null hypothesis) were true, there
would be a 0.00% chance of obtaining results that fit Full
Model (the alternative hypothesis) so well.
Since the P value is less than the traditional significance
level of 5%, you can conclude that the data fit
significantly better to Full Model than to Linear Model.
Thanks to the nice folks at GraphPad
Conclusions
In Greenwood, Unincorporated Baltimore County, MD, USA this
model supports the hypothesis that sunspots influence
average annual temperature in the time period studied.
There is no evidence of a significant linear warming trend
since 1892.
Limitations
As on previous pages....
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