Linear Regression in R: A Mangrove Example

Linear regression is one of the most commonly used tools in mangrove and forestry research — for example, to build allometric equations that predict tree height, biomass, or carbon stock from an easy-to-measure variable like stem diameter. This mini-course walks through fitting a simple linear regression in R, step by step.

What you need

• R installed on your computer.
• Optionally, RStudio as a more convenient editor — not required, base R works fine for this lesson.

No prior statistics background is assumed beyond knowing what a scatter plot is.

The example data

To keep this lesson self-contained, we’ll use a small illustrative dataset relating stem diameter at breast height (DBH, in cm) to tree height (in m) for ten hypothetical mangrove trees. This is teaching data only — not a real field survey — but the code below works the same way once you replace it with your own measurements.

mangrove <- data.frame(
  dbh_cm = c(4.2, 6.1, 7.8, 9.0, 10.5, 12.3, 13.7, 15.1, 16.8, 18.2),
  height_m = c(3.1, 4.0, 4.8, 5.3, 6.0, 6.7, 7.2, 7.9, 8.5, 9.1)
)
mangrove

Step 1: Look at the data first

Always plot before you model.

plot(
  height_m ~ dbh_cm,
  data = mangrove,
  xlab = "Diameter at breast height (cm)",
  ylab = "Height (m)",
  pch = 19
)

A roughly straight-line pattern like this is what makes linear regression a reasonable choice here.

Step 2: Fit the model

In R, a linear regression is fit with lm(). The formula height_m ~ dbh_cm reads as “height explained by diameter”:

model <- lm(height_m ~ dbh_cm, data = mangrove)
summary(model)

The summary() output gives you, among other things:

• Coefficients — the intercept and slope of the fitted line. The slope tells you how much height increases, on average, for each 1 cm increase in diameter.
• Pr(>|t|) — the p-value for each coefficient; a small value (typically < 0.05) suggests the relationship is unlikely to be due to chance alone.
• Multiple R-squared — the proportion of variation in height explained by diameter (0 to 1; closer to 1 means a tighter fit).

Step 3: Draw the fitted line

plot(
  height_m ~ dbh_cm,
  data = mangrove,
  xlab = "Diameter at breast height (cm)",
  ylab = "Height (m)",
  pch = 19
)
abline(model, col = "forestgreen", lwd = 2)

Step 4: Check the residuals

Before trusting the model, it’s good practice to glance at the residual plots — they help you spot patterns the straight line missed:

par(mfrow = c(2, 2))
plot(model)
par(mfrow = c(1, 1))

Look especially at “Residuals vs Fitted”: if the points scatter randomly around the horizontal zero line with no obvious curve, a straight-line fit is reasonable.

Using your own field data

Once you’re comfortable with the steps above, swap the example data.frame for your own measurements — typically imported from a CSV file:

mangrove <- read.csv("my_field_data.csv")

As long as your CSV has a dbh_cm and height_m column (or you adjust the column names in the code above to match yours), everything else works the same way.

Where to go next

This lesson covers a single predictor variable. Real allometric models often use a log-transformed diameter, or add a second predictor (like wood density), which is where multiple regression (lm(y ~ x1 + x2)) comes in — a natural next topic for a future mini-course.