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Lowess smoothing is a technique used to fit a non-linear regression model to a set of data points. It is implemented in R with the lowess() function. To use the lowess() function, the user must specify a vector of x values, a vector of y values, and a fraction between 0 and 1 that will determine the degree of smoothing. The lowess() function will then output a smoothed curve that can be plotted over the original data points to provide a smoother, more accurate representation of the data.
In statistics, the term lowess refers to “locally weighted scatterplot smoothing” – the process of producing a smooth curve that fits the data points in a scatterplot.
To perform lowess smoothing in R we can use the lowess() function, which uses the following syntax:
lowess(x, y, f = 2/3)
where:
- x: A numerical vector of x values.
- y: A numerical vector of y values.
- f: The value for the smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values result in more smoothness.
The following step-by-step example shows how to perform lowess smoothing for a given dataset in R.
Step 1: Create the Data
First, let’s create a fake dataset:
df <- data.frame(x=c(1, 1, 2, 2, 3, 4, 6, 6, 7, 8, 10, 11, 11, 12, 13, 14), y=c(4, 7, 9, 10, 14, 15, 19, 16, 17, 21, 22, 34, 44, 40, 43, 45))
Step 2: Plot the Data
Next, let’s plot the x and y values from the dataset:
plot(df$x, df$y)
Step 3: Plot the Lowess Curve
Next, let’s plot the lowess smoothing curve over the points in the scatterplot:
#create scatterplot plot(df$x, df$y) #add lowess smoothing curve to plot lines(lowess(df$x, df$y), col='red')
Step 4: Adjust the Smoother Span (Optional)
We can also adjust the f argument in the lowess() function to increase or decrease the value used for the smoother span.
Note that the larger the value we provide, the smoother the lowess curve will be.
#create scatterplot plot(df$x, df$y) #add lowess smoothing curves lines(lowess(df$x, df$y), col='red') lines(lowess(df$x, df$y, f=0.3), col='purple') lines(lowess(df$x, df$y, f=3), col='steelblue') #add legend to plot legend('topleft', col = c('red', 'purple', 'steelblue'), lwd = 2, c('Smoother = 1', 'Smoother = 0.3', 'Smoother = 3'))
