In addition, the regression
of a linear trend model can produce a coefficient of determination, r ².
Not exact matches
Tests for
trend with the use
of simple
linear regression analysis were performed by
modeling the median values
of each fiber category as a continuous variable.
Tests
of linear trend across categories
of coffee consumption were performed by assigning participants the midpoint
of their coffee - consumption category and entering this new variable into a separate Cox proportional - hazards regression
model.
The relationship between an athlete personal best in competition and back squat, bench press and power clean 1RM was determined via general
linear model polynomial contrast analysis and regression for a group
of 53 collegiate elite level throwers (24 males and 29 females); data analysis showed significant
linear and quadratic
trends for distance and 1RM power clean for both male (
linear: p ≤ 0.001, quadratic: p ≤ 0.003) and female (
linear: p ≤ 0.001, quadratic: p = 0.001) suggesting how the use
of Olympic - style weightlifting movements — the clean, in this particular case, but more in general explosive, fast, athletic - like movements — can be a much better alternative for sport - specific testing for shot putters (Judge, et al, 2013).
A test for
linear trend of effects across coffee consumption categories was performed by regressing each log RR on the ordered categorical variable for coffee in 5 levels using a random - effect meta - regression
model.
While using a percent growth rate for free cash flows might be conventional, mathematically convenient and easier to convey to others, it is not as accurate or conservative as using an absolute rate
of change from a
linear trend model.
The
model in F&R is elegantly simple and does a good job
of showing that a
linear trend due to CO2 + a few forcings that we know to be operant and important are sufficient to explain most
of the variability in all
of the temperature datasets.
One baseline
model is a simple
linear trend from the start
of the century.
The DSLPA index computed from HadSLP2 shows a much more «
trend - like» reduction than the datasets shown in the manuscript, in which the 1970s shift plays a less pivotal role; though the amplitude
of slope
of the
linear trend is consistent with the
model and observations.
I looked at eight CMIP 5
models whose output I had ready access to and calculated
linear trends of potential intensity over the period 2006 - 2100 under the RCP 8.5 emissions pathway.
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.
Also, about 2/3
of the individual ensemble - members (46 out
of 68) from all the
model runs have
linear trends that indicate at least a nominal weakening — this is significantly different from what one would be expected from a Binomial distribution with a 50 % probability.
Canadian Ice Service, 4.7, Multiple Methods As with CIS contributions in June 2009, 2010, and 2011, the 2012 forecast was derived using a combination
of three methods: 1) a qualitative heuristic method based on observed end -
of - winter arctic ice thicknesses and extents, as well as an examination
of Surface Air Temperature (SAT), Sea Level Pressure (SLP) and vector wind anomaly patterns and
trends; 2) an experimental Optimal Filtering Based (OFB)
Model, which uses an optimal
linear data filter to extrapolate NSIDC's September Arctic Ice Extent time series into the future; and 3) an experimental Multiple
Linear Regression (MLR) prediction system that tests ocean, atmosphere and sea ice predictors.
Canadian Ice Service, 4.7 (+ / - 0.2), Heuristic / Statistical (same as June) The 2015 forecast was derived by considering a combination
of methods: 1) a qualitative heuristic method based on observed end -
of - winter Arctic ice thickness extents, as well as winter Surface Air Temperature, Sea Level Pressure and vector wind anomaly patterns and
trends; 2) a simple statistical method, Optimal Filtering Based
Model (OFBM), that uses an optimal
linear data filter to extrapolate the September sea ice extent timeseries into the future and 3) a Multiple
Linear Regression (MLR) prediction system that tests ocean, atmosphere and sea ice predictors.
Over 1900 — 2005 the observed
trend is substantially greater than the
model expectation: a probability
of 87 % for the
linear trend compared with 78 % for the robust
trend.
Over 1950 — 2005, the observed warming
trend is slightly greater than the
model expectation: a probability
of 57 % for the
linear trend compared with 61 % for the robust
trend.
Because their
model is insensitive to the small
linear trends in GSL over the Common Era, the relative heights
of the 300-1000 CE and 20th century peaks are not comparable.
The critical phrase seems to be «Because their
model is insensitive to the small
linear trends in GSL over the Common Era, the relative heights
of the 300-1000 CE and 20th century peaks are not comparable.»
Box 9.2 Climate
Models and the Hiatus in Global Mean Surface Warming
of the Past 15 Years «The observed global mean surface temperature (GMST) has shown a much smaller increasing
linear trend over the past 15 years than over the past 30 to 60 years (Section 2.4.3, Figure 2.20, Table 2.7; Figure 9.8; Box 9.2 Figure 1a, c).
Without a validated
model there is no justification for fitting a
linear trend and extrapolation way outside the range
of the data.
Canadian Ice Service; 5.0; Statistical As with Canadian Ice Service (CIS) contributions in June 2009 and June 2010, the 2011 forecast was derived using a combination
of three methods: 1) a qualitative heuristic method based on observed end -
of - winter Arctic Multi-Year Ice (MYI) extents, as well as an examination
of Surface Air Temperature (SAT), Sea Level Pressure (SLP) and vector wind anomaly patterns and
trends; 2) an experimental Optimal Filtering Based (OFB)
Model which uses an optimal
linear data filter to extrapolate NSIDC's September Arctic Ice Extent time series into the future; and 3) an experimental Multiple
Linear Regression (MLR) prediction system that tests ocean, atmosphere, and sea ice predictors.
Canadian Ice Service, 4.7 (± 0.2), Heuristic / Statistical (same as June) The 2015 forecast was derived by considering a combination
of methods: 1) a qualitative heuristic method based on observed end -
of - winter Arctic ice thickness extents, as well as winter Surface Air Temperature, Sea Level Pressure and vector wind anomaly patterns and
trends; 2) a simple statistical method, Optimal Filtering Based
Model (OFBM), that uses an optimal
linear data filter to extrapolate the September sea ice extent timeseries into the future and 3) a Multiple
Linear Regression (MLR) prediction system that tests ocean, atmosphere and sea ice predictors.
The
models used in climate science are based not on extrapolated
linear trends, but on expected consequences
of all known physical forcings — which are not periodic.
The
trends for all
of the scenarios for the period 2000 - 2040 are effectively
linear, similar to or lower than the
trend 1997 - 2000 that informed the
model start point, and on the scale
of the predicted 0.2 C increase there is no variability to speak
of in any
of them.
The long periods found in dT / dt are different since a
linear trend is accommodated by the constant rate
of change «c» in the
model.
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.
A generalized nonlinear mixed
model was used for
modeling temporal
trends of tree mortality and recruitment rates, and a
linear mixed
model was used for
modeling temporal
trends of tree growth rates (Methods).
Figure 1: Heat content smoothed with 1 -2-1 filter and overlaid with
linear trend portion
of best - fit
model (slope = -0.35 x 1022 J / yr)
But the real L&S
model failure is in the
linear trend, since these mysterious astronomical cycles are simply oscillations on top
of that
trend.
The magnitude
of each relative changepoint is calculated using the most appropriate two - phase regression
model (e.g., a jump in mean with no
trend in the series, a jump in mean within a general
linear trend, etc.).
So this
model will produce a
linear warming
trend with two natural oscillations superimposed on top
of it.
Past climate
models, as judged by the performance
of the majority
of Coupled
Model Intercomparison Project 3 (CMIP3) simulations used in the IPCC Fourth Assessment Report, underestimated the observed
linear trend in Arctic sea ice loss (Stroeve et al., 2007).
Absent an exponential temperature rise signaling forcing synergies in progress, seeing a
linear trend for five decades leads to deep discounting
of models that need to get to a degree per decade in order to make 2100 as hot as some have claimed over the last half century.
«In response to those who complained in my recent post that
linear trends are not a good way to compare the
models to observations (even though the modelers have claimed that it's the long - term behavior
of the
models we should focus on, not individual years), here are running 5 - year averages for the tropical tropospheric temperature,
models versus observations...»
In fact, you can get a very good fit with actual temperature by
modeling them as three functions: A 63 - year sine wave, a 0.4 C per century long - term
linear trend (e.g. recovery from the little ice age) and a new
trend starting in 1945
of an additional 0.35 C, possibly from manmade CO2.
The historical record
of our climate is seems pretty clearly to follow a sin wave, yet all the
models attempt to predict a dynamic, cyclical climate using
linear trends.
Fit a
linear model (preferably with ARMA (1,1) noise as the noise process is autocorrelated), the
trend is the slope
of that
linear model (i.e. the coeffcient
of the
linear term
of the
model).
However, it is instructive to note that a simple
model of a
linear trend plus sine wave matches history so well, particularly since it assumes such a small contribution from CO2 (yet matches history well) and since in prior IPCC reports, the IPCC and most modelers simply refused to include cyclic functions like AMO and PDO in their
models.
Trends in rates
of child diagnoses by mother's response level in children with a baseline diagnosis and in rates
of incidence or relapse in children without a baseline diagnoses were examined separately using the Cochran - Armitage test for
trend.29 Low event rates precluded fitting regression
models adjusting for potential confounders, such as age and sex
of child, using generalized
linear models with an identity - link function, to estimate parameters for adjusted
trends.
Intervention effects will be assessed by conducting
linear and logistic random effects
models incorporating a time by group interaction or latent growth curve
modelling to determine whether
trends across the three data points within the course
of the patients» treatment differ between the carer groups.39 The
models will adjust for confounders and effect modifiers as necessary.
Conditional latent growth
model results show that having adversity is positively associated with the intercept, but negatively associated with the
linear trend of changes
of depressive symptoms in adolescence (p <.01).