This document analyzes relationships between environmental change indicators during the Quaternary period using regression analysis. It uses proxy data from loess/paleosol sequences in China, deep sea sediments in the east Pacific, and ice cores from East Antarctica to represent glacial/interglacial cycles. Exploratory analysis, interpolation, and multiple regression methods were used to analyze relationships between the proxy records over the middle to late Pleistocene. Results found weaker correlations between soil properties and climate cycles compared to other proxies. Logistic regression also suggested temporal variability in relationships between climate change factors and sediment properties.

1. Regression analysis of
relations among
Quaternary environmental
change indicators
Pavel Samec

2. Content
• Introduction
- Glacial/interglacial cycles
- The polyglacism theory
• Material
- Loess/paleosol proxy series
- Deep-sea mud proxy series
- Ice core proxy series
• Methods
- Exploratory data analysis
- Interpolation
- Multiple regression
- Logistic regression
• Results and Discussion
• Summary
• References

3. Introduction
The Quaternary is a period when the geological presence has developed.
The Quaternary Period is characterized by regular alternation of major
environmental changes with the intensity of glacial/interglacial.
• The glacial is an event of glaciations characterized by expansion of continental and
mountain glaciers, global marine regression, global reduction of vegetation biomass and
expansion of terrestrial sedimentary environments.
• The interglacial is an event of interglaciations characterized by minimal glaciations, global
marine transgression, global growth of vegetation biomass and an intensive soil
formation ont the most of land.
The polyglacism theory deals with common variability of marine and
terrestrial sedimentation features in relation to the variability of the
external physical environment that indicate the global impacts of multiple
oscillations glacial/interglacial.
The aim of the study was using of the logistic regression for better
description of assumed polyglacial relationships.

4. Material
• Data
- Loess/paleosol series (Chinese Loess Plateau; 6.9-0 Ma; Sun et al. 2012)
- Deep sea d18O (East Pacific; 470-4 Ka; Lea et al. 2000)
- Ice core (East Antarctica; 803-2 Ka; Barnola et al. 1999; Petit et al. 2000)
• Analysed periods
- Middle-Upper Pleistocene (470-12 Ka)
- Upper Pleistocene – Holocene (126-1 Ka)

5. The Central Chinese Loess Plateau eolian sediment magnetic
susceptibility (MS) (data according to Sun et al. 2012).
350
300
250
200
150
100
50
0
6.8 6.4 6.0 5.7 5.4 5.1 4.9 4.6 4.1 3.8 3.6 3.2 3.0 2.7 2.4 2.1 1.7 1.5 1.2 0.9 0.6 0.3 0.0
MS (10-8 m3/kg)
Dating (Ma)
The East Equatorial Pacific average sea surface temperatures and
oxygen proxy record (data according to Lea et a. 2000).
d18O T (°C)
3
2
1
0
-1
-2
-3
32
28
24
20
16
461 384 306 245 176 124 80 36 4
Dating (Ka)
sea surface temperature
oxygen isotopical signal

6. Methods
• Global temperature deviations were main features of the
glacial/interglacial cycle.
• Glacial – 0
• Interglacial - 1
DT (°C) CO2 (ppm)
4
2
0
-2
-4
-6
-8
-10
300
280
260
240
220
200
180
314 231 136 2
carbon dioxide (ppm) Dating (Ka)
temperature deviations
(°C)
CO2 (ppm)
300
275
250
225
200
175
150
-10 -8 -6 -4 -2 0 2
DT (°C)
North Atlantic
East Equatorial Pacific
Antarctica
dCO2
1.00
0.75
0.50
0.25
0.00
0.00 0.30 0.60 0.90 1.20 1.50
Ttropy/Tpolar

7. • Exploratory data analysis
- Test on normality distribution
- Regression diagnosis
- Linear correlation and regression
• Interpolation
- Transformation according to 0-1 limits
• Regression analysis
- Linear regression
- Multiple regression
- Logistic regression
Data calibration
EDA
Linear regression
Binomical
interpolation
Multiple regression Logistic regression

8. Results and discussion
Exploratory linear regression of basic Quaternary sedimentation core
properties. y – receptor; x – predictor; F –Fischer-Snedecorov’s testing
criterion; t – Student’s t-test criterion; r ‒ correlation coefficient; SC –
Scott’s test on multicolinearity; C-W – Cook-Weisberg’s test on
heteroscedasticity; J-B – Jarque-Berrae’s test on normality of residues;
Wa – Wald’s test on autocorrelation.

9. Linear regression of the compared facial proxy data

10. Multiple regression of compared environmetal proxy indicators
Multiple regression of basic
Quaternary sea (d18O) and terrestrial
environmental indicators (CaCO3).
SD – standard deviation; B-CT –
Box-Cox transformation; MS –
magnetic susceptibility; GSM – grain
size median.

11. Logistic regression of compared environmental proxy indicators

12. Summary
• Changes in the basic soil properties of a loess/paleosol sequences reliably
do not indicate changes in the intensity of glacial/interglacial cycles
between the Middle and Upper Pleistocene.
• Changes in the basic soil properties of a loess/paleosol sequences have
been reflecting climatic changes statistically more significantly than the
deep-sea sedimentation since the Upper Pleistocene (cycle eem‒visla) .
• Correlations of atmospheric CO2 and surface temperatures are greater
than correlation of other polyglacial phenomenas.
• Linear regression revealed on the assumption that the dependences of soil
properties were smaller than polyglacial relations of other environmental
indicators.
• Logistic regression suggested that temporal variability in feedbacks
between climatic change predictors and properties of forming sediments
may be cause of the lack of a simple Quaternary climatic change
indication.

13. References
• BARNOLA J.M. et al. (1999): Historical CO2 record from the Vostok ice core. In:
Trends: A Compendium of Data on Global Change. U. S. Department of Energy Oak
Ridge.
• HEIKKINEN R.K. et al. (2006): Methods and uncertainties in bioclimatic envelope
modelling under climate change. Progress in Physical Geography 30: 6751‒6777.
• KUKLA J. (1978): The Classical European Glacial Stages: Correlation with deep-sea
sediments. Transactions of the Nebraska Academy of Science 6: 57–93.
• KUKLA G., CÍLEK V. (1996): Plio-Pleistocene megacycles: record of climate and
tectonics. Palaeogeography, Palaeoclimatology, Palaeoecology 120: 171‒194.
• LEA D.W. et al. (2000): Climate impact of late Quaternary equatorial Pacific sea
surface temperature variations. Science 289: 1719–1724.
• OSBORN J. W. (2010): Improving your data transformation: Applying the Box-Cox
transformation. Practical Assessment, Research & Evaluation 15: 2‒9.
• PETIT J.R. (1999): Climate and atmospheric history of the past 420,000 years from
the Vostok ice core, Antarctica. Nature 399: 429–436.
• SUN Y. (2012): Seven million years of wind and precipitation variability on the
Chinese Loess Plateau. Earth and Planetary Science Letters 297: 525–535.