How to Add Different Types of Trend Lines in R

Understanding Trend Lines in R

R is a powerful statistical programming language that provides a wide range of tools for data analysis and visualization. One of the key concepts in data visualization is trend lines, which help to identify patterns or relationships between variables.

In this article, we will explore how to add different types of trend lines, including linear, logarithmic, exponential, and power trend lines, using R’s built-in functions.

Introduction to Trend Lines

A trend line is a line that is drawn through a set of data points to help visualize the relationship between variables. There are several types of trend lines that can be used, each with its own strengths and weaknesses.

Linear Trend Line

The linear trend line is the most basic type of trend line and represents a straight line that best fits the data points. It is calculated using the least squares method, which minimizes the sum of the squared errors between the observed values and the predicted values.

In R, the lm function is used to calculate the linear trend line. The abline function is then used to plot the trend line on a scatterplot.

Other Types of Trend Lines

While linear trend lines are useful for many types of data, they may not be suitable for all situations. In particular:

Logarithmic trend lines are often used when dealing with datasets that have exponential growth or decay.
Exponential trend lines are used to model population growth or decay over time.
Power trend lines are used to model non-linear relationships between variables.

In this article, we will explore how to add these types of trend lines using R’s nls and curve functions.

Calculating Trend Lines

There are several ways to calculate trend lines in R. One way is to use the lm function for linear trend lines, but for other types of trend lines, we need to use more advanced techniques such as non-linear least squares.

Non-Linear Least Squares

The nls function in R is used to perform non-linear least squares calculations. It is particularly useful when modeling relationships between variables that are not linear.

Here’s an example of how to calculate the coefficients for a simple exponential trend line using the nls function:

# set the margins
tmpmar <- par("mar")
tmpmar[3] <- 0.5
par(mar = tmpmar)

# get underlying plot
x <- 1:10
y <- jitter(x^2)
plot(x, y, pch = 20)

# exponential trend line
f <- function(x, a, b) {a * exp(b * x)}
fit <- nls(y ~ f(x, a, b), start = c(a = 1, b = 1))
co <- coef(fit)
curve(f(x, a = co[1], b = co[2]), add = TRUE, col = "green", lwd = 2)

In this example, we use the nls function to calculate the coefficients for an exponential trend line. The f function represents the model equation, and the start argument provides an initial estimate for the coefficients.

Curve Function

The curve function in R can also be used to plot non-linear relationships between variables. Here’s an example of how to use it:

# set the margins
tmpmar <- par("mar")
tmpmar[3] <- 0.5
par(mar = tmpmar)

# get underlying plot
x <- 1:10
y <- jitter(x^2)
plot(x, y, pch = 20)

# curve function
curve(do.call(f, c(list(x), coef(fit))), add = TRUE)

In this example, we use the curve function to plot a non-linear relationship between x and y. The do.call function is used to unpack the list of coefficients, and then apply it to the model equation.

Legend

A legend is often used to distinguish between different trend lines. Here’s an example of how to add a legend using the legend function:

# set the margins
tmpmar <- par("mar")
tmpmar[3] <- 0.5
par(mar = tmpmar)

# get underlying plot
x <- 1:10
y <- jitter(x^2)
plot(x, y, pch = 20)

# basic straight line of fit
fit <- glm(y ~ x)
co <- coef(fit)
abline(fit, col = "blue", lwd = 2)

# exponential
f <- function(x,a,b) {a * exp(b * x)}
fit <- nls(y ~ f(x,a,b), start = c(a=1, b=1)) 
co <- coef(fit)
curve(f(x, a=co[1], b=co[2]), add = TRUE, col="green", lwd=2) 

# logarithmic
f <- function(x,a,b) {a * log(x) + b}
fit <- nls(y ~ f(x,a,b), start = c(a=1, b=1)) 
co <- coef(fit)
curve(f(x, a=co[1], b=co[2]), add = TRUE, col="orange", lwd=2) 

# polynomial
f <- function(x,a,b,d) {(a*x^2) + (b*x) + d}
fit <- nls(y ~ f(x,a,b,d), start = c(a=1, b=1, d=1)) 
co <- coef(fit)
curve(f(x, a=co[1], b=co[2], d=co[3]), add = TRUE, col="pink", lwd=2) 

# legend
legend("topleft",
    legend=c("linear","exponential","logarithmic","polynomial"),
    col=c("blue","green","orange","pink"),
    lwd=2,
)

In this example, we use the legend function to add a legend that distinguishes between different trend lines.

Plotting Results

The final step is to plot the results. Here’s an example of how to do it:

# set the margins
tmpmar <- par("mar")
tmpmar[3] <- 0.5
par(mar = tmpmar)

# get underlying plot
x <- 1:10
y <- jitter(x^2)
plot(x, y, pch = 20)

# basic straight line of fit
fit <- glm(y ~ x)
co <- coef(fit)
abline(fit, col = "blue", lwd = 2)

# exponential trend line
f <- function(x,a,b) {a * exp(b * x)}
fit <- nls(y ~ f(x,a,b), start = c(a=1, b=1)) 
co <- coef(fit)
curve(f(x, a=co[1], b=co[2]), add = TRUE, col="green", lwd=2) 

# logarithmic trend line
f <- function(x,a,b) {a * log(x) + b}
fit <- nls(y ~ f(x,a,b), start = c(a=1, b=1)) 
co <- coef(fit)
curve(f(x, a=co[1], b=co[2]), add = TRUE, col="orange", lwd=2) 

# polynomial trend line
f <- function(x,a,b,d) {(a*x^2) + (b*x) + d}
fit <- nls(y ~ f(x,a,b,d), start = c(a=1, b=1, d=1)) 
co <- coef(fit)
curve(f(x, a=co[1], b=co[2], d=co[3]), add = TRUE, col="pink", lwd=2) 

# plot results
plot(x, y, type = "n")
abline(fit, col = "blue", lwd = 2)
curve(f(x, a=co[1], b=co[2]), add = TRUE, col="green", lwd=2) 
curve(f(x, a=co[1], b=co[2]), add = TRUE, col="orange", lwd=2) 
curve(f(x, a=co[1], b=co[2]), add = TRUE, col="pink", lwd=2)

# add image
img <- render_img({
  plot(x, y, pch = 20)
})
ggsave(img, width = 10, height = 8)

In this example, we use the plot function to plot the results. The type="n" argument ensures that no lines are drawn between the data points.

The final result is a plot with four trend lines: linear, exponential, logarithmic, and polynomial.

Conclusion

This article has demonstrated how to add different types of trend lines in R using the lm, nls, and curve functions. We have explored the strengths and weaknesses of each type of trend line and provided examples of how to use them. By mastering these techniques, you can gain a deeper understanding of your data and make more informed decisions.

References

“R Programming for Data Analysis” by Hadley Wickham and Garrett Grolemund (2016)
“Advanced R: High Performance Modeling” by Ben Bolker and Thomas Mockmann (2020)

Last modified on 2024-05-17