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table of Contents
Introduction
Below is an example of species diversity shows how the correlation analysis and linear regression analysis in the R language.
How to do the test
Correlation and linear regression examples
Data = read.table(textConnection(Input),header=TRUE)
Simple graph data
plot(Species ~ Latitude,
data=Data,
pch=16,
xlab = "Latitude",
ylab = "Species") 
Correlation
You can use cor.test function. It can perform Pearson, Kendall and Spearman correlation.
Pearson correlation
Pearson correlation is related to the most common form. Assumed that the data are linearly related, and the residuals were normally distributed.
cor.test( ~ Species + Latitude,
data=Data,
method = "pearson",
conf.level = 0.95)
Pearson's product-moment correlation
t = -2.0225, df = 15, p-value = 0.06134
cor
-0.4628844
Kendall related
Kendall's rank correlation is a nonparametric test, it is not assumed that the distribution of data or data are linearly related. It ranked data to determine the degree of correlation.
cor.test( ~ Species + Latitude,
data=Data,
method = "kendall",
continuity = FALSE,
conf.level = 0.95)
Kendall's rank correlation tau
z = -1.3234, p-value = 0.1857
tau
-0.2388326
Spearman
Spearman rank correlation is a nonparametric test, it is not assumed that the distribution of data or data are linearly related. It sorts the data to determine the degree of correlation, and in order for the measurement.
Linear Regression
Linear regression can be used lm perform the function. You can use lmrob perform robust regression function.
summary(model) # shows parameter estimates,
# p-value for model, r-square
Estimate Std. Error t value Pr(>|t|)
(Intercept) 585.145 230.024 2.544 0.0225 *
Latitude -12.039 5.953 -2.022 0.0613 .
Multiple R-squared: 0.2143, Adjusted R-squared: 0.1619
F-statistic: 4.09 on 1 and 15 DF, p-value: 0.06134
Response: Species
Sum Sq Df F value Pr(>F)
Latitude 1096.6 1 4.0903 0.06134 .
Residuals 4021.4 15
Draw linear regression
plot(Species ~ Latitude,
data = Data,
pch=16,
xlab = "Latitude",
ylab = "Species")
abline(int, slope,
lty=1, lwd=2, col="blue") # style and color of line
Check the model assumptions
Linear Model residuals histogram. These residuals should be approximately normally distributed.
Graph of residuals versus predicted values. Residuals should be unbiased and evenly.
Robust Regression
The linear regression is not sensitive to outliers in the response variable.
summary(model) # shows parameter estimates, r-square
Estimate Std. Error t value Pr(>|t|)
(Intercept) 568.830 230.203 2.471 0.0259 *
Latitude -11.619 5.912 -1.966 0.0681 .
Multiple R-squared: 0.1846, Adjusted R-squared: 0.1302
anova(model, model.null) # shows p-value for model
pseudoDf Test.Stat Df Pr(>chisq)
1 15
2 16 3.8634 1 0.04935 *
Drawing model
Examples of linear regression
summary(model) # shows parameter estimates,
# p-value for model, r-square
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 12.6890 4.2009 3.021 0.0056 **
Weight 1.6017 0.6176 2.593 0.0154 *
Multiple R-squared: 0.2055, Adjusted R-squared: 0.175
F-statistic: 6.726 on 1 and 26 DF, p-value: 0.0154
### Neither the r-squared nor the p-value agrees with what is reported
### in the Handbook.
library(car)
Anova(model, type="II") # shows p-value for effects in model
Sum Sq Df F value Pr(>F)
Weight 93.89 1 6.7258 0.0154 *
Residuals 362.96 26
# # #
Power Analysis
Correlation power analysis
### --------------------------------------------------------------
### Power analysis, correlation
### --------------------------------------------------------------
pwr.r.test()
approximate correlation power calculation (arctangh transformation)
n = 28.87376
If you have any questions, please leave a comment below.
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