Why would I wish to do that when it's more robust to
fit a trend line L to the data D that minimizes the standard deviation of the residual, D minus L?
The r - squared of a linear trend line of this partial Sine wave is 0.88... 88 % of the data
fit the trend line.
The argument is that if
you fit a trend line from 1975 to the start of 1997 (or the middle of 1997, the exact time not making much difference) then an extension of that trendline to the present shows that the data since then has not deviated in any significant way from that trendline.
Now what do we suppose might happen if
we fit a trend line to this data?
PHEaston: as a scientist, why are you picking ANY arbitrary start and end dates in noisy data sets, rather than
fitting trend lines (preferably with error ranges)?
Re # 209 I think it's funny, because look at how much of that «trend» literature does not bother to plot standard errors,
fitted trend lines, confidence intervals.
With the former the only thing that can be achieved is
fitting a trend line (the parameter being its slope, assuming centered data).
But can you point to a half century at any time in the past millennium where
fitting a trend line gives a slope (up or down) of anywhere near a degree per century (0.01 degrees per year or 0.1 degrees per decade)?
For myself, I think that 200 years from now,
the fitted trend line on the graph of CET as it appears in the Year 2200 edition of Wikipedia is likely to be roughly at 10.3 C in the year 2200, or about 0.6 C higher than in 2007; and that GMT will have followed roughly that same upward trend.
Not exact matches
But a single straight
line still neatly
fits the jagged upward
trend of temperature of the past 40 to 50 years.
This best -
fit line follows the same
trend into the future and can be used to project the change of the climate variable in the coming years.
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There will be
trends evident in some of the scatterplots, to which they could add
lines of best
fit either «by eye» or using a spreadsheet.
Fitting with national
trends, teachers frequently move across state or district
lines and change positions within and across sectors.
In
line with current
trends, a reversing camera and rear parking sensors are
fitted as standard, which means teachers unfamiliar with bus driving duties can manoeuvre with confidence.
Data plotted ready for pupils to add
lines of best
fit and describe correlation, a speedy introduction into the concept of data
trends.
Together, these different
trends resulted in the shallower slope of the red
line that was
fit to the data.
Finally, I see that the eyeball
line of best
fit through the model outputs on the 30 - year graph implies a
trend of approximately 1.5 C degrees per century.
There was a slight
trend if I
fit a straight
line to the data, but it was too slight to be significant.
Just in case you think this is a new
trend, consider this flashback to the 1980's, which shows how the public - service aspect of journalism — sustaining coverage of important arenas even if it does not «sell» — is a hard
fit in a world focused on the bottom
line:
I went to the trouble of
fitting a linear
trend line to the A2 model input
line from 2002 - 2009 and obtained a correlation coefficient (R2) of 0.99967.
In other words, he
fit a straight
line to the 2002 - 2009 data and extrapolated to the year 2100, at which time the
trend predicts a CO2 concentration of 575 ppm.
The green
line is the best
fitting trend.
The solid
line is is simply a
fit 4th degree polynomial I imposed in the a spirit of parsimony to illustrate
trend in a general way.
The best -
fitting quadratic
trend is shown (green
line).
The green
line is the best
fitting quadratic
trend.
If I go out and measure something, anything, and plot the points of a piece of graph paper, and the points may lie on a straight
line, some sort of curve, or there may be so much noise in the data that no
trend is apparent, then this is what
fits the data.
AGW theory can never be reduced to a falsifiable hypothesis and therefore has no practical utility outside of making something that is unimaginably complex appear simple: like,
fitting a least squares
trend -
line to a haze of points.
The RealClimate
trend line starts about 1993, so let's take the data from 1993 through 2002 and
fit a straight
line, then extend that
line as a prediction through 2010.
Pennsylvania anthracite has a single
trend line with a single normal
fit.
You could also question why to
fit linear model but since climatology seems obsessed with «
trends» I though this was better than a single straight
line.
What do you think of drawing a straight
line fit through wiggly noisy data and calling it a
trend?
Concerning the derivation of my own graphical adaptations of the IPCC and Hadley Center source graphics, the process by which the slopes of historical CET
trend lines were determined is readily evident from direct examination of the illustration, without any further explanation other than to clarify that all
fitting of
trend slopes was done by visually placing each linearized
trend line onto the original HadCET source plot wherever it was appropriate in the CET record for the particular decadal rate of change being
fitted: -0.1, -0.03, +.03, +0.1, +0.2, +0.3, or +0.4
The
fit of a
trend line to the time series of global - mean surface temperature (e.g., Figure 2.5) indicates a warming between 0.25 to 0.4 °C for this 20 - year period, or approximately 0.1 to 0.2 °C per decade, 6 depending upon which of the existing data sets is used to represent the surface temperatures, and exactly how the
fitting is done.
Time series of global - mean surface temperature from 1979 to 1998, repeated from Figure 2.3, shown with a
trend line fitted by the method of ordinary least squares.
There appears to be an overall decline, as indicated by the blue
line, which is a linear regression
fit to estimate the overall
trend.
The last two Decembers (2009 and 2010) have high (but not the highest) values, and the smooth
fit (red
line) suggests a possible upward
trend, especially recently.
Third, and tying into the second point, the
trend line should have indications for standard error, meaning there is more room around that
line where you can
fit «valid»
trends both above and below it.
The best
fit linear
trend lines (not shown) of the model mean and all datasets are set to zero at 1979, which is the first year of the satellite data.
That temperature anomalies that contain a
trend do not
fit a normal distribution well should, in my view, not be surprising since the random scatter is around the
trend line.
It regurgitates NSIDC graphs, complete with
lines of best
fit that reveal the underlying downward
trend towards inevitable oblivion, without wondering why scientific predictions from the NSIDC and elsewhere about the future of Arctic ice are spread across a whole continent of ball parks each the size of Wales.
A running mean merely smooths, it doesn't give a
trend line, unlike linear regression, meaning least - squares
fit of a straight
line.
Linear
fits to climate: I have seen some terrible attempts to
fit trends to a straight
line, such as for climate sensitivity studies..
Therefore I
fit, to the data since 1995, a straight
line to model the
trend, and a 4th - order Fourier
fit to model the annual cycle:
This band width was signal was normalized and the
trend removed by
fitting an order 2 polynomial
trend line to the band width data.
However, it's hardly endearing to see a
trend line presented with no pretense of an effort to generate some r ^ 2, and to propose explanations that may account for its value, or equivalent means to quantify the
fit of the hypothesis to the data.