An example of statistical data analysis using the R ...

1 Tutorial:An example of statistical data analysisusing the R environment for statistical computingD G RossiterVersion ; May 6, 2017llllllll1020304050607080102030405060 7080 Topsoil clay %Subsoil clay %Subsoil vs. topsoil clay, by zonel1234 Slopes:zone 1 : 2 : 3 : 4 : : 15 10 5051015 Regression Residuals vs. Fitted Values, subsoil clay %FittedResidual1781119128137138139145660 0006700006800006900007000003150003200003 25000330000335000340000 GLS 2nd order trend surface, subsoil clay %ENCopyright D G Rossiter 2008 2010, 2014, 2017 All rights reserved.

2 Repro-duction and dissemination of the work as a whole (not parts) freely permitted ifthis original copyright notice is included. Sale or placement on a web site wherepayment must be made to access this document is strictly prohibited. To adaptor translate please contact the author Introduction12 example Data Loading the dataset .. A normalized database structure* ..53 Research questions84 Univariarte Univariarte Exploratory Data analysis .. Point estimation; inference of the mean.

3 Answers ..155 Bivariate correlation and Conceptual issues in correlation and regression .. Bivariate Exploratory Data analysis .. Bivariate Correlation analysis .. Fitting a regression line .. Bivariate Linear Regression .. Bivariate Regression analysis from scratch* .. Regression diagnostics .. to observed data .. residuals .. of residuals .. * .. * .. Prediction .. Robust regression* .. Structural analysis * .. Structural analysis by Principal Components*.

4 A more difficult case .. Non-parametric correlation .. Answers ..536 One-way analysis of Variance (ANOVA) Exploratory Data analysis .. One-way ANOVA .. ANOVA as a linear model* .. Means separation* .. One-way ANOVA from scratch* .. Answers ..667 Multivariate correlation and Multiple Correlation analysis .. simple correlations .. partial correlations .. Multiple Regression analysis .. Comparing regression models .. regression models with the adjustedR2.

5 Regression models with the AIC .. regression models with ANOVA .. Stepwise multiple regression* .. Combining discrete and continuous predictors .. Diagnosing multi-colinearity .. Visualising parallel regression* .. Interactions* .. analysis of covariance* .. Design matrices for combined models* .. Answers ..968 Factor Principal components analysis .. synthetic variables* .. * .. * .. * .. Factor analysis * .. Answers .. 1179 Postplots.

6 Trend surfaces .. Higher-order trend surfaces .. Local spatial dependence and Ordinary Kriging .. objects .. of local spatial structure .. by Ordinary Kriging .. Answers .. 13810 Going further140 References141 Index of R concepts146A Derivation of the hat Influence of values on prediction .. 147ii1 IntroductionThis tutorial presents a data analysis sequence which may be applied to en- vironmental datasets, using a small but typical data set of multivariate pointobservations.

7 It is aimed at students in geo-information application fields whohave some experience with basic statistics, but not necessarily with statisticalcomputing. Five aspects are emphasised:1. Placing statistical analysis in the framework of research questions;2. Moving from simple to complex methods: first exploration, then selectionof promising modelling approaches;3. Visualising as well as computing;4. Making correct inferences;5. statistical computation and analysis is carried out in the R environment for statistical computing andvisualisation [16], which is an open-source dialect of the S statistical computinglanguage.

8 It is free, runs on most computing platforms, and contains contribu-tions from top computational statisticians. If you are unfamiliar with R, see themonograph Introduction to the R Project for statistical Computing for use atITC [30], the R Project s introduction to R [28], or one of the many tutorialsavailable via the R web help is available for all R methods using the?methodsyntax at thecommand prompt; for example ?lmopens a window with help for thelm(fitlinear models) :These notes use R rather than one of the many commercial statisticsprograms because R is a completestatistical computing environment, based ona modern computing language (accessible to the user), and with packages con-tributed by leading computational statisticians.

9 R allows unlimited flexibility andsophistication. Press the button and fill in the box is certainly faster but aswith Windows word processors, what you see isallyou get . With R it may bea bit harder at first to do simple things, but you are not limited. R is completelyfree, can be freely-distributed, runs on all desktop computing platforms, is regu-larly updated, is well-documented both by the developers and users, is the subjectof several good statistical computing texts, and has an active user introductory textbook with similar intent to these notes, but with a wider setof examples, is by Dalgaard [7].

10 A more advanced text, with many interestingapplications, is by Venables and Ripley [35]. Fox [12] is an extensive explanationof regression modelling; the companion Fox and Weisberg [14] shows how to useR for this, mostly with social sciences tutorial follows a data analysis problem typical of earth sciences, natural andwater resources, and agriculture, proceeding from visualisation and explorationthrough univariate point estimation, bivariate correlation and regression analysis ,multivariate factor analysis , analysis of variance, and finally some each section, there are sometasks.