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The apparent discrepancy between this joinpoint analysis and the modest decrease shown in Table 2 and Figure 2a may be explained by the rather wide dispersion of annual data points.
With only 5 annual data points there was insufficient data to perform a longitudinal analysis of individual students through time.
Although the number of beds and involuntary admissions was large, the number of annual data points included in the analyses was relatively small (20 for cross lagged analyses).
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In our experiments, the set of training data Otrain (used in the procedure of learning) contained the 2016 annual data (366 data points) and the set of testing data Otest from 2017.1.1~ 2017.1.7 (7 data points).
And the World Energy Council (representing 30,000 members in 93 countries, including governments and businesses) has this year incorporated into its energy sustainability index (in its World Energy Trilemma annual report) data points on access to electricity and its reliability and availability.
There were 1 478 149 annual PM2.5 data points from 1999 to 2009 coming from 1576 monitoring stations.
To calculate the annual change (20 data points) we carried out de-trending by introducing one degree of differencing.
CIs were much narrower than for the annual data estimates, and point estimates for age-specific and cause-specific deaths showed clear pattern of higher relative risks in the elderly and in deaths due to cardiovascular and especially respiratory diseases.
Experts have cautioned against reading too much into annual data, while others have pointed to the dramatic decline in crime over the past quarter-century to support the argument for criminal-justice restructuring.
The first step in our analysis was determining the annual AOPD based on experimental data points.
We estimated annual trends using the available data points to compare across countries despite this limitation; a sensitivity analysis computing trends from 2000 to 2008 showed that our results were robust to the choice of period.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com