REGRESSION ANALYSIS OF LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION
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1 REGRESSION ANALYSIS OF LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION STATISTICAL REPORT Prepared for Shanti Berryman Woods Buffalo Environmental Association Moab, Utah May 2003 by Pacific Analytics PO Box 219 Albany, OR (541)
2 REGRESSION ANALYSIS OF LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION STATISTICAL REPORT Prepared by: Pacific Analytics, L.L.C. Post Office Box 219 Albany, Oregon Tel. (541) Gregory Brenner Senior Associate / Project Manager
3 Table of Contents REGRESSION ANALYSIS OF LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION STATISTICAL REPORT I. TABLE OF CONTENTS I. Table of Contents... 1 II. Executive Summary... 2 III. Introduction... 3 Questions of Interest... 4 Species of Interest... 4 Elements... 4 IV. Statistical Procedures... 5 V. Cladina mitis VI. Evernia mesomorpha VII. Hypogymnia physodes VIII. Literature Cited Statistical Report by Pacific Analytics, L.L.C. 1
4 Executive Summary II. EXECUTIVE SUMMARY This is a report of regression analysis of Lichen Data from the Athabasca Oil Sands Region. The report answers three general questions of interest for each of 28 elements. The Questions of Interest are: 1. Do the concentrations of elements in lichens change with distance from mine sites? 2. Do the concentrations of elements in lichens change with direction along a transect? 3. Is there an interaction effect between distance and direction? The report includes an introduction to the analysis, a description of the statistical procedures, and the results of the analyses. The results are presented in three chapters, one dealing with each species. Statistical Report by Pacific Analytics, L.L.C. 2
5 Introduction III. INTRODUCTION Lichens are a unique life form, consisting of a relationship between a fungus and a photosynthetic partner, a cyanobacterium or a green alga. The association is said to be symbiotic, such that the fungus provides moisture and shelter for the algal cells allowing them live even in places that otherwise would be unsuitable for them. Due to this symbiotic relationship, lichens are able to live in some of the harshest habitats on earth. Lichens are extremely widespread in nature; they occur from arid desert regions to the Arctic and grow on bare soil, tree trunks, and rocks. Lichens grow very slowly, often less than a millimeter per year. Lichens lack any outside covering, or cuticle, and consequently are directly exposed to the atmosphere, which they depend upon for their nutrients and water. Moistened lichen tissues act as blotters, soaking up chemicals or materials deposited on their surfaces. This feature has also made them highly susceptible to air pollutants; and lichens are perhaps the plant species most susceptible to sulfur dioxide, heavy metals, and acid rain. Since lichens are very sensitive to pollutants, they are sometimes used as indicators of air and water pollution. Lichens are investigated at a number of locations surrounding a point or area pollution source, or at a number of locations within an area of interest. Appropriate lichen metrics are recorded at each location and are related to known or inferred pollution levels. The metrics include distribution of individual indicator species, frequency or abundance of individual species, species Statistical Report by Pacific Analytics, L.L.C. 3
6 Introduction richness (total number of different species) at each study location, total lichen cover, and element content in lichen samples. In this study lichens were used as bioindicators of air pollution in the Athabasca Oil Sands region. Concentrations of elements in lichens are used to assess the effects of direction and distance from a point source on element deposition. Questions of Interest 1. Do the concentrations of elements in lichens change with distance from mine sites? 2. Do the concentrations of elements in lichens change with direction along a transect? 3. Is there an interaction effect between distance and direction? Species of Interest Element content was measured from three lichen species: 1 Clamit = Cladina mitis 2 Evemes = Evernia mesomorpha 3 Hypphy = Hypogymnia physodes Elements Twenty-nine elements were detected in laboratory analysis: Percent Nitrogen, Percent Sulfur, parts per million (ppb for Hg) of Al, As, B, Ba, Be, Ca, Cd, Co, Cr, Cu, Fe, Hg, K, Li, Mg, Mn, Mo, Na, Ni, P, Pb, Rb, Si, Sr, Ti, V, Zn. Statistical Report by Pacific Analytics, L.L.C. 4
7 Statistical Procedures IV. STATISTICAL PROCEDURES Data Reduction The sampling units in this study are the sites at which lichen samples were collected. In most cases more than one sample of each species was taken at a site. These field replicate samples are sub-samples of the sampling unit and are not appropriate for analysis without accounting for the structure of the sampling. For this study, the site mean response of the sub-samples for each element for each species was calculated and used as the response variable for that site. Twenty-nine elements were detected in laboratory analysis. In each of the species, some of the samples had element concentrations below the detectable limit. Statistical analysis was not conducted for those elements that had greater than about 40% of the samples below detectable limits. These include lithium (Li), beryllium (Be), cobalt (Co), and rubidium (Rb) for all three species. For the same reason, statistical analysis was not performed for arsenic (As) and lead (Pb) in C. mitis and E. mesomorpha. Linear Regression Regression analysis describes statistical relationships between a response variable and several explanatory variables. In the case of lichen data, the response variables are the measurements of element Statistical Report by Pacific Analytics, L.L.C. 5
8 Statistical Procedures concentration in lichen samples taken at several sites. The explanatory variables are cardinal directions and distance from mine sites. Knowledge about the statistical relationship between variables enables one to determine certain characteristics of the response variable from the measured explanatory variables. In mathematical terms the relationship looks like μ = β 0 + β 1 X 1 + β 2 X 2 where μ = the mean of the response distribution, β 0 is the intercept coefficient, β 1 is the coefficient for the first explanatory variable, X 1, and β 2 is the coefficient for the next explanatory variable, X 2. The regression coefficients are calculated using Least Squares Estimation. These parameters are estimated and each has its own associated standard error. An estimate for the value of the response variable can be calculated by inserting the values of the explanatory variables into the equation. The difference between the estimated value and the observed measured value is called the residual. The Least Squares Estimation procedure minimizes the squared residuals while estimating the regression coefficients. There are several conditions under which Least Squares Estimation is most efficient. The first is that the response distributions for each set of explanatory values have approximately the same standard deviations. The next is that the distributions of the response variables are approximately Normal (Gaussian). The third is that each response is drawn independently of all the other responses. Statistical Report by Pacific Analytics, L.L.C. 6
9 Statistical Procedures Least Squares Regression is useful for modeling the fit of a response variable to several continuous explanatory variables. In this study, the distance from mine sites is one such continuous variable. Least Squares Regression can also be used to distinguish between two or more groups or categories. Indicator (or Dummy) variables are set up for each of the groups (or levels of a factor) but one. The indicator variables take on values of 1 or 0, indicating the attribute is present or absent. This method was used in this study for the analysis of the effect of direction on the concentration of elements in lichens. When the explanatory variables are categorical, statistical analysis may be accomplished by regression or analysis of variance. The choice between the two methods is straightforward: if the simple linear regression model fits then it is preferred. The regression approach has the advantage of allowing interpolation, it provides more degrees of freedom for error estimation, and it yields smaller standard errors for the estimates of the mean responses. The fit of the model to the assumptions can be assessed by residual plots. These are the graph of the residuals on the Y axis and the fitted values on the X axis. Inequalities of standard error are easily detected from these graphs. Usually transformations (e.g., log or square root transformations) will correct for departures from equality. In other cases, different distributions may more accurately model the data. One distribution used in this study was the Poisson Distribution. Statistical Report by Pacific Analytics, L.L.C. 7
10 Statistical Procedures Poisson Regression The Poisson probability distribution is useful for describing the population distribution of counts of occurrences of some event over time or space, but has been used in a wide variety of situations. It can be useful for modeling distributions that do not fit the Normal distribution used in linear regression. The distribution is based on the number of successes over a given measurement period. The probability of obtaining Y successes is given by the formula Probability{Y} = exp(-μ)*μy/y!, for any Y = 0,1,2, The features of the Poisson distribution allow regression models to account for increasing variance with increasing means response. In the Poisson distribution, the variance is equal to the mean. Poisson log-linear regression models specify that the logarithms of means of Poisson responses are linear in regression coefficients. Coefficients of the Poisson regression model can be estimated using a generalized linear model. The generalized linear model (glm) with a Poisson response is log(μ) = β0 + β1 X1 + β2 X2 where μ = the mean of the Poisson distribution, β0 is the intercept coefficient, β1 is the coefficient for the first explanatory variable, X1, and β2 is the coefficient for the next explanatory variable, X2. Statistical Report by Pacific Analytics, L.L.C. 8
11 Statistical Procedures Many times analysis of Poisson distributed data is conducted with transformed data. The logarithm of the response often straightens out the relationship between the response and the explanatory variables. The variance remains non-constant and normal regression analysis often fails to arrive at a parsimonious model. The transformation that stabilizes the variance is the square root of the response, but interpretation is not satisfactory. The Poisson log-linear approach does not require a transformation. The maximum likelihood method is used to estimate the coefficients in Poisson log-linear regression. The parameters for the model are those that yield the highest probability of observing precisely what was observed. The method is calculation intensive and is used in most modern statistical software packages. A thorough discussion of Generalized Linear Regression and Maximum Likelihood Estimation of model parameters is contained in Generalized Linear Models 2nd Edition (McCullagh and Nelder 1991). Software used for Poisson log-linear regression was S-Plus version 4.5 (MathSoft ). Statistical Report by Pacific Analytics, L.L.C. 9
12 CLADINA MITIS V. CLADINA MITIS N% Linear Regression N% Regression Table: Coefficients Value Std. Error t value P-value Intercept dirne dirns dirnw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is N% Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the percent of N in Cladina mitis lichen samples. There is no evidence that the percent of N in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the percent of N in Cladina mitis lichen samples is smaller in the East direction than in the North direction (p-value = ). There is suggestive evidence that the percent of N in Cladina mitis lichen samples is smaller in the West direction than in the North direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 10
13 CLADINA MITIS N% Linear Regression Residual Plot: fit1a$residuals fit1a$fitted.values Statistical Report by Pacific Analytics, L.L.C. 11
14 CLADINA MITIS S% S% Linear Regression: S% Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 12
15 CLADINA MITIS S% Log Transformed Analysis: S% Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws dirne dirns Cdistance dirwecdistance dirwncdistance dirwscdistance Residual standard error: on 32 degrees of freedom Multiple R-Squared: F-statistic: on 7 and 32 degrees of freedom, the P- value is S% Statistical Inference: There is evidence of an interaction effect between distance from mine sites and direction on the percent of S in Cladina mitis lichen samples. The percent S decreases more slowly in the South and East direction than in the West direction (p-values = and respectively). There is strong evidence that the percent of S in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 13
16 CLADINA MITIS S% Log Transformed Regression Residual Plot: fit1a$residuals fit1a$fitted.values Statistical Report by Pacific Analytics, L.L.C. 14
17 CLADINA MITIS Al ppm Al ppm Linear Regression Al ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 15
18 CLADINA MITIS Al ppm Log Transformation: Al ppm Log Transformed Residual Plot: fit1a$residuals fit1a$fitted.values Statistical Report by Pacific Analytics, L.L.C. 16
19 CLADINA MITIS Al ppm Rank Transformation Al ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirse dirsn dirsw dirnw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: 26.2 on 4 and 35 degrees of freedom, the P- value is 4.218e-010 Al ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Al ppm in Cladina mitis lichen samples. There is strong evidence that the Al ppm in Cladina mitis lichen samples declines as the distance from mine sites increases (p-value < ). There is evidence that the Al ppm in Cladina mitis lichen samples is smaller in the West direction than in the North direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 17
20 CLADINA MITIS Al ppm Rank Transformed Residual Plot: fit3b$residuals fit3b$fitted.values Statistical Report by Pacific Analytics, L.L.C. 18
21 CLADINA MITIS B ppm B ppm Linear Regression B ppm Linear Regression Residual Plot fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 19
22 CLADINA MITIS B ppm Log Transformation B ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirse dirsn dirsw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is B ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the B ppm in Cladina mitis lichen samples. There is strong evidence that the B ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is no evidence that the B ppm in Cladina mitis lichen samples is smaller any direction. Statistical Report by Pacific Analytics, L.L.C. 20
23 CLADINA MITIS B ppm Log Transformed Residual Plot fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 21
24 CLADINA MITIS Ba ppm Ba ppm Linear Regression Ba ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 22
25 CLADINA MITIS Ba ppm Log Transformation Ba ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 23
26 CLADINA MITIS Ba ppm Generalized Linear Models: Ba ppm Poisson Regression Table: Coefficients Value Std. Error t value P-value Intercept NA dirse NA dirsn NA dirsw NA Cdistance Null Deviance: on 39 degrees of freedom Residual Deviance: on 35 degrees of freedom Ba ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Ba ppm in Cladina mitis lichen samples. There is strong evidence that the Ba ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the Ba ppm in Cladina mitis lichen samples is different on different directional transects (p-value = ). This p-value is derived from the drop-in-deviance test of the directional explanatory factor. Statistical Report by Pacific Analytics, L.L.C. 24
27 CLADINA MITIS Ca ppm Ca ppm Linear Regression Ca ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 25
28 CLADINA MITIS Ca ppm Log Transformation Ca ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is Ca ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Ca ppm in Cladina mitis lichen samples. There is strong evidence that the Ca ppm in Cladina mitis lichen samples decreases with increasing distance from mine sites (p-value < ). There is evidence that the Ca ppm in Cladina mitis lichen samples is smaller in the East direction than in the North, South and West directions (p-values = , respectively). Statistical Report by Pacific Analytics, L.L.C. 26
29 CLADINA MITIS Ca ppm Log Transformed Residual Plot: fit2a$residuals fit2a$fitted.values Statistical Report by Pacific Analytics, L.L.C. 27
30 CLADINA MITIS Cd ppm Cd ppm Linear Regression Cd ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 28
31 CLADINA MITIS Cd ppm Log Transformation Cd ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance dirwecdistance dirwncdistance dirwscdistance Residual standard error: on 31 degrees of freedom Multiple R-Squared: F-statistic: 2.77 on 7 and 31 degrees of freedom, the P- value is Cd ppm Statistical Inference: There is strong evidence of an interaction effect between distance from mine sites and direction on the Cd ppm in Cladina mitis lichen samples. The Cd ppm decreases more rapidly in the West direction than in the East, North, and South directions (p-value = , , and respectively). There is strong evidence that the Cd ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (pvalue = ). Statistical Report by Pacific Analytics, L.L.C. 29
32 CLADINA MITIS Cd ppm Log Transformed Residual Plot: fit2a$residuals fit2a$fitted.values Statistical Report by Pacific Analytics, L.L.C. 30
33 CLADINA MITIS Cr ppm Cr ppm Linear Regression Cr ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 31
34 CLADINA MITIS Cr ppm Log Transformation Cr ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance direncdistance direscdistance direwcdistance Residual standard error: on 32 degrees of freedom Multiple R-Squared: F-statistic: on 7 and 32 degrees of freedom, the P- value is Cr ppm Statistical Inference: There is evidence of an interaction effect between distance from mine sites and direction on the Cr ppm in Cladina mitis lichen samples. The Cr ppm decreases more rapidly in the West direction than in the East direction (p-value = ). There is no evidence that the Cr ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 32
35 CLADINA MITIS Cr ppm Log Transformed Residual Plot: fit2a$residuals fit2a$fitted.values Statistical Report by Pacific Analytics, L.L.C. 33
36 CLADINA MITIS Cu ppm Cu ppm Linear Regression Cu ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 34
37 CLADINA MITIS Cu ppm Log Transformation Cu ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is Cu ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Cu ppm in Cladina mitis lichen samples. There is strong evidence that the Cu ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the Cu ppm in Cladina mitis lichen samples is smaller in the East direction than in the North direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 35
38 CLADINA MITIS Cu ppm Log Transformed Residual Plot: fit2a$residuals fit2a$fitted.values Statistical Report by Pacific Analytics, L.L.C. 36
39 CLADINA MITIS Fe ppm Fe ppm Linear Regression Fe ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 37
40 CLADINA MITIS Fe ppm Log Transformation Fe ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 38
41 CLADINA MITIS Fe ppm Rank Transformation Fe ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is 9.344e-012 Fe ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Fe ppm in Cladina mitis lichen samples. There is strong evidence that the Fe ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value < ). There is no evidence that the Fe ppm in Cladina mitis lichen samples is different in any direction. Statistical Report by Pacific Analytics, L.L.C. 39
42 CLADINA MITIS Fe ppm Rank Transformed Residual Plot: fit3$residuals fit3$fitted.values Statistical Report by Pacific Analytics, L.L.C. 40
43 CLADINA MITIS Hg ppb Hg ppb Linear Regression: Hg ppb Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: 5.9 on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the p- value is Statistical Inference: There is no evidence of an interaction effect between distance from the mine and direction on the Hg ppb in Cladina mitis lichen samples. There is no evidence that the Hg ppb in Cladina mitis lichen samples is different in any direction. There is no evidence that the Hg ppb in Cladina mitis lichen samples changes with the distance from the mine. Statistical Report by Pacific Analytics, L.L.C. 41
44 CLADINA MITIS Hg ppb Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 42
45 CLADINA MITIS K ppm K ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is K ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the K ppm in Cladina mitis lichen samples. There is suggestive evidence that the K ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the K ppm in Cladina mitis lichen samples is smaller in the East direction than in the North direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 43
46 CLADINA MITIS K ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 44
47 CLADINA MITIS Mg ppm Mg ppm Linear Regression Mg ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 45
48 CLADINA MITIS Mg ppm Log Transformation Mg ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is Mg ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Mg ppm in Cladina mitis lichen samples. There is strong evidence that the Mg ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the Mg ppm in Cladina mitis lichen samples is smaller in the East direction than in the North, South, and West directions (p-value = , , and respectively). Statistical Report by Pacific Analytics, L.L.C. 46
49 CLADINA MITIS Mg ppm Log transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 47
50 CLADINA MITIS Mn ppm Mn ppm Linear Regression Mn ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirne dirns dirnw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is 3.721e-007 Mn ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Mn ppm in Cladina mitis lichen samples. There is strong evidence that the Mn ppm in Cladina mitis lichen samples increases as the distance from mine sites increases (p-value < ). There is suggestive evidence that the Mn ppm in Cladina mitis lichen samples is greater in the West direction than in the North direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 48
51 CLADINA MITIS Mn ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 49
52 CLADINA MITIS Mo ppm Mo ppm Linear Regression Mo ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 50
53 CLADINA MITIS Mo ppm Log Transformation Mo ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 51
54 CLADINA MITIS Mo ppm Rank Transformation Mo ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirne dirns dirnw Cdistance Residual standard error: on 32 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is Mo ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Mo ppm in Cladina mitis lichen samples. There is strong evidence that the Mo ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is no evidence that the Mo ppm in Cladina mitis lichen samples is different in any direction. Statistical Report by Pacific Analytics, L.L.C. 52
55 CLADINA MITIS Mo ppm Rank Transformed Residual Plot: fit3$residuals fit3$fitted.values Statistical Report by Pacific Analytics, L.L.C. 53
56 CLADINA MITIS Na ppm Na ppm Linear Regression Na ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 54
57 CLADINA MITIS Na ppm Rank Transformation Na ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws dirns Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is 4.798e-006 Na ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Na ppm in Cladina mitis lichen samples. There is strong evidence that the Na ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value < ). There is evidence that the Na ppm in Cladina mitis lichen samples is smaller in the West direction than in the South direction (p-value = ). There is evidence that the Na ppm in Cladina mitis lichen samples is smaller in the North direction than in the South direction (pvalue = ). Statistical Report by Pacific Analytics, L.L.C. 55
58 CLADINA MITIS Na ppm Rank Transformed Residual Plot: fit3$residuals fit3$fitted.values Statistical Report by Pacific Analytics, L.L.C. 56
59 CLADINA MITIS Ni ppm Ni ppm Linear Regression Ni ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 57
60 CLADINA MITIS Ni ppm Log Transformation Ni ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance direncdistance direscdistance direwcdistance Residual standard error: on 32 degrees of freedom Multiple R-Squared: F-statistic: on 7 and 32 degrees of freedom, the P- value is Ni ppm Statistical Inference: There is evidence of an interaction effect between distance from mine sites and direction on the Ni ppm in Cladina mitis lichen samples. The Ni ppm decreases more rapidly in the West direction than in the East direction (p-value = ). There is no evidence that the Ni ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 58
61 CLADINA MITIS Ni ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 59
62 CLADINA MITIS P ppm P ppm Linear Regression P ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirne dirns dirnw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is P ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the P ppm in Cladina mitis lichen samples. There is no evidence that the P ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the P ppm in Cladina mitis lichen samples is smaller in the East direction than in the North direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 60
63 CLADINA MITIS P ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 61
64 CLADINA MITIS Si ppm Si ppm Linear Regression Si ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 62
65 CLADINA MITIS Si ppm Log Transformation Si ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance direncdistance direscdistance direwcdistance Residual standard error: on 32 degrees of freedom Multiple R-Squared: F-statistic: on 7 and 32 degrees of freedom, the P- value is 4.794e-009 Si ppm Statistical Inference: There is evidence of an interaction effect between distance from mine sites and direction on the Si ppm in Cladina mitis lichen samples. The Si ppm decreases more rapidly in the North direction than in the East direction (p-value = ). There is evidence that the Si ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 63
66 CLADINA MITIS Si ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 64
67 CLADINA MITIS Sr ppm Sr ppm Linear Regression Sr ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 65
68 CLADINA MITIS Sr ppm Log Transformation Sr ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is Sr ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Sr ppm in Cladina mitis lichen samples. There is strong evidence that the Sr ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is no evidence that the Sr ppm in Cladina mitis lichen samples is different in any direction. Statistical Report by Pacific Analytics, L.L.C. 66
69 CLADINA MITIS Sr ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 67
70 CLADINA MITIS Ti ppm Ti ppm Linear Regression Ti ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 68
71 CLADINA MITIS Ti ppm Log Transformation Ti ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirne dirns dirnw Cdistance dirnecdistance dirnscdistance dirnwcdistance direwcdistance Residual standard error: on 32 degrees of freedom Multiple R-Squared: F-statistic: 9.53 on 7 and 32 degrees of freedom, the P- value is 2.392e-006 Ti ppm Statistical Inference: There is evidence of an interaction effect between distance from mine sites and direction on the Ti ppm in Cladina mitis lichen samples. The Ti ppm decreases more rapidly in the North and West directions than in the East direction (p-values = and respectively). There is evidence that the Ti ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value < ). Statistical Report by Pacific Analytics, L.L.C. 69
72 CLADINA MITIS Ti ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 70
73 CLADINA MITIS V ppm V ppm Linear Regression V ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 71
74 CLADINA MITIS V ppm Log Transformation V ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 72
75 CLADINA MITIS V ppm Rank Transformation V ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is 4.767e-011 V ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the V ppm in Cladina mitis lichen samples. There is strong evidence that the V ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value < ). There is evidence that the V ppm in Cladina mitis lichen samples is smaller in the West direction than in the North, South, and East directions (p-value = , , and respectively). Statistical Report by Pacific Analytics, L.L.C. 73
76 CLADINA MITIS V ppm Rank Transformed Residual Plot: fit3$residuals fit3$fitted.values Statistical Report by Pacific Analytics, L.L.C. 74
77 CLADINA MITIS Zn ppm Zn ppm Linear Regression Zn ppm Linear Regression Residual Plot: fit3$residuals fit3$fitted.values Statistical Report by Pacific Analytics, L.L.C. 75
78 CLADINA MITIS Zn ppm Log Transformation Zn ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 35 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 35 degrees of freedom, the P- value is Zn ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Zn ppm in Cladina mitis lichen samples. There is no evidence that the Zn ppm in Cladina mitis lichen samples decreases as the distance from mine sites increases (p-value = ). There is no evidence that the Zn ppm in Cladina mitis lichen samples is different in any direction. Statistical Report by Pacific Analytics, L.L.C. 76
79 CLADINA MITIS Zn ppm Log Transformed Residual Plot: fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 77
80 EVERNIA MESOMORPHA VI. Evernia mesomorpha N% N% Linear Regression N% Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 23 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 23 degrees of freedom, the P- value is N% Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the percent of N in Evernia mesomorpha lichen samples. There is evidence that the percent of N in Evernia mesomorpha lichen samples decreases as the distance from mine sites increases (pvalue = ). There is no evidence that the percent of N in Evernia mesomorpha lichen samples is different in any direction Statistical Report by Pacific Analytics, L.L.C. 78
81 EVERNIA MESOMORPHA N% Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 79
82 EVERNIA MESOMORPHA S% S% Linear Regression: S% Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 23 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 23 degrees of freedom, the P- value is S% Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the percent of S in Evernia mesomorpha lichen samples. There is strong evidence that the percent of S in Evernia mesomorpha lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the percent of S in Evernia mesomorpha lichen samples is greater in the East and North directions than in the West direction (p-value = and respectively). Statistical Report by Pacific Analytics, L.L.C. 80
83 EVERNIA MESOMORPHA S% Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 81
84 EVERNIA MESOMORPHA Al ppm Al ppm Linear Regression Al ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 23 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 23 degrees of freedom, the P- value is Al ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Al ppm in Evernia mesomorpha lichen samples. There is strong evidence that the Al ppm in Evernia mesomorpha lichen samples declines as the distance from mine sites increases (p-value = ). There is evidence that the Al ppm in Evernia mesomorpha lichen samples is smaller in the West direction than in the North and East directions (p-value = and respectively). Statistical Report by Pacific Analytics, L.L.C. 82
85 EVERNIA MESOMORPHA Al ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 83
86 EVERNIA MESOMORPHA B ppm B ppm Linear Regression B ppm Linear Regression Residual Plot fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 84
87 EVERNIA MESOMORPHA B ppm Log Transformation B ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept diren dires direw Cdistance Residual standard error: on 23 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 23 degrees of freedom, the P- value is B ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the B ppm in Evernia mesomorpha lichen samples. There is strong evidence that the B ppm in Evernia mesomorpha lichen samples decreases as the distance from mine sites increases (p-value < ). There is no evidence that the B ppm in Evernia mesomorpha lichen samples is different in any direction. Statistical Report by Pacific Analytics, L.L.C. 85
88 EVERNIA MESOMORPHA B ppm Log Transformed Residual Plot fit2$residuals fit2$fitted.values Statistical Report by Pacific Analytics, L.L.C. 86
89 EVERNIA MESOMORPHA Ba ppm Ba ppm Linear Regression Ba ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 23 degrees of freedom Multiple R-Squared: F-statistic: on 4 and 23 degrees of freedom, the P- value is Ba ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Ba ppm in Evernia mesomorpha lichen samples. There is strong evidence that the Ba ppm in Evernia mesomorpha lichen samples decreases as the distance from mine sites increases (p-value = ). There is evidence that the Ba ppm in Evernia mesomorpha lichen samples is greater in the North direction than in the West direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 87
90 EVERNIA MESOMORPHA Ba ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 88
91 EVERNIA MESOMORPHA Ca ppm Ca ppm Linear Regression Ca ppm Linear Regression Residual Plot: fit1$residuals fit1$fitted.values Statistical Report by Pacific Analytics, L.L.C. 89
92 EVERNIA MESOMORPHA Ca ppm Log Transformation Ca ppm Regression Table: Coefficients Value Std. Error t value P-value Intercept dirwe dirwn dirws Cdistance Residual standard error: on 23 degrees of freedom Multiple R-Squared: F-statistic: 8.5 on 4 and 23 degrees of freedom, the P- value is Ca ppm Statistical Inference: There is no evidence of an interaction effect between distance from mine sites and direction on the Ca ppm in Evernia mesomorpha lichen samples. There is strong evidence that the Ca ppm in Evernia mesomorpha lichen samples decreases with increasing distance from mine sites (p-value = ). There is evidence that the Ca ppm in Evernia mesomorpha lichen samples is smaller in the West direction than in the North direction (p-value = ). Statistical Report by Pacific Analytics, L.L.C. 90
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«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.»
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