Analysis of Linear Regression Plots

Analysis of Linear Regression Plots
0 to 50th Percentile:
Most of the southwestern part of the region shows a decrease in precipitation by
around 10%, where some places see decreases as high as 20%. However, 50th percentile
values are at or near zero in this region, making these decreases trivial. Where the
decrease is more significant is east the USA over the gulf stream, where 50th percentile
values are relatively high. The extreme southeast over the Atlantic Ocean, as well as
northern and eastern parts of the landmass show weaker decreases, while many other of
these locations show moderate increases of between 4 and 6 percent. One location in the
north has an increase of about 7%. The median land and water change is -3.2% (for land
only it is -2.2%) and r2 values are quite high nearly everywhere (median 0.99).
50th to 80th Percentile:
The general southwest and southern parts of the region continue to show
decreases in this percentile range, but the magnitudes of these changes is slightly
damped. The north and east general region show little change to increases as high as
about 4%. 80th percentile values over the southwest are still essentially near zero, making
the decreases in precipitation here unsubstantial. The median land and water change is 2.1%, whereas it is near zero over the land exclusively, implying that ocean regions will
see a greater reduction in precipitation in this range. R2 values remain very high almost
everywhere (median 0.99), only dropping below 0.90 over the central Pacific coast.
80th to 97th Percentile:
The southwest still shows decreases in precipitation per degree K by about 5 to 10
percent. At this point, values of precipitation within this bin begin to generally emerge
above zero, making this change more significant. The southeast of the region shows little
change to slight decreases. The northern half of the region generally expresses increases
on the order of 2 to 4 percent. The median change for land and water is about 1.1%
(larger for land only at 2.6%) and r2 values are still very high everywhere (median 0.99),
with no locations dropping below 0.90.
97th to 99th Percentile:
The southern third of the region generally shows little change to slight decreases
as high as 2%. An exception is the extreme southwest over the eastern Pacific Ocean,
which shows increases at 4 to 8 percent. The northern half of the region shows
widespread increases of 2 to 7%, which are more significant to the northeast. Over the
northeast coast of the US and adjacent Atlantic Ocean, as well as the Pacific northwest,
these increases are more meaningful because percentile values in this range are the
relatively high. The median change for this bin is 3.2% for land and water (3.6% for
land) and r2 values are generally higher to the north more mediocre to the south with a
median of 0.98.
99th to 100th Percentile:
Changes range from about 0 to 20% with the highest increases (between 10 and
20%) over central and western Mexico and the eastern Pacific. Across the north and east,
precipitation increases between 4 and 8 percent nearly everywhere. The median change
is 5.5% over land and water (5.3% over land), and r2 values are high to the north and
become noticeably weaker to the south, dropping to as low as 0.65 along the extreme
southern border of the region. The median r2 value is 0.96.
99.7th to 100th Percentile:
Precipitation increases nearly everywhere at rates from about 1% to 25%. The
highest increases are on the west coast and southern portions of Mexico and adjacent
eastern Pacific. Much of the northeastern part of the region sees increases ranging from 6
to 10%. Only one location near eastern Colorado does not see a change. The median
changes are 6.1% over land only and 6.5% over land and water. R2 values do not follow
any particular pattern, but are generally higher to the north and lower to the south, where
values are consistently less than 0.50. The median land r2 value is 0.94 while that for
land and water is 0.93.
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