##### Code for Testing Assumptions of Regression in R

### Import data


datum=read.csv(file.choose()) ### creates a data frame named datum from imported csv file


### check data was imported properly


head(datum) ### column headers of data file plus first 6 rows of data 
summary(datum) ### summary statistics for datum


### Run a regression - Generic Code - Procedures below require you to run a regression first


results=lm(Y~X,data=datum) ### runs a linear regression between 'Y' and 'X' columns in 'datum', calls results 'results'
summary(results)


#####Testing of assumptions

###continuous variable - no need to test, should be obvious


###ScatterPlot - Good for testing all assumptions


plot(Y~X,data=datum)
abline(results) ###plots line over data
# if non-linear relationship, will have groups of points above and below line
# if heteroscedastic data, variance in error will not be constant across x values
# if non-normally distributed residuals, error will be skewed above or below the line
# if autocorrelated data, points will seem to follow each other in a path


### Plot of Residuals - Good for testing all assumptions


residuals(results) #### provides residual error of points
plot(residuals(results)~datum$X) ###plot residuals in order of X values
# line is now horizontal at Y = 0
# if non-linear relationship, will have groups of points above and below line
# if heteroscedastic data, variance in error will not be constant across x values
# if non-normally distributed residuals, error will be skewed above or below the line
# if autocorrelated data, points will seem to follow each other in a path


### Histogram of residuals - Good for testing normality assumption
# Note that this is testing whether residuals are global normal (across all x), not whether residuals are locally normal


help(hist) # help file for histograms
hist(residuals(results)) ### draws a histogram of residuals
hist(residuals(results),breaks=10) ### the 'breaks' argument changes the number of bars
# if non-normally distributed residuals, histogram will appear non-normal


#### autocorrelation function

help(acf) #help file for autocorrelation function
acf(residuals(results)) ### runs autocorrelation function on residuals from regression
# to test for autocorrelation, residuals must be in order that autocorrelation might exist (usually x-order)
acf(residuals(results)[order(datum$X)]) ###[order(datum$Rainfall)] ### sorts residuals into x-order
# if autocorrelated data, lines at x=1,2,3,.... will cross dotted horizontal line, indicated significant autocorrelation
# Note that violating assumption of non-linearity can also appear as autocorrelation.