How to Calculate Correlation Coefficient (r) and Create a Scatter Plot in R Studio

Introduction: Understanding Correlation and Its Importance in Data Analysis

In statistics, understanding relationships between variables is crucial for data interpretation, decision-making, and predictive modeling. One of the most common and powerful tools for this is the correlation coefficient (r), which measures the strength and direction of a linear relationship between two continuous variables.

This tutorial will guide you through calculating the Pearson correlation coefficient in R Studio, using a practical example of height and weight data, and visualizing the relationship using a scatter plot with a regression line.

By the end of this post, you’ll be able to:

•     Calculate correlation in R
•     Interpret correlation results
•     Create a scatter plot in R
•     Add a regression line and annotate your plot
•     Understand how to use visualizations in exploratory data analysis (EDA)

What Is the Correlation Coefficient (r)?

Definition of Pearson’s Correlation Coefficient

The Pearson correlation coefficient (r) is a measure of the linear association between two continuous variables. It ranges from -1 to +1:

• r = +1: Perfect positive linear relationship
• r = -1: Perfect negative linear relationship
• r = 0: No linear relationship

Formula for Pearson’s r

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$$

$$Dataset\; Used\; for\; Correlation\; Analysis$$

$$Here,\; we’ll\; use\; a\; sample\; dataset\; representing\; height\; (cm)\; and\; weight\; (kg)\; of\; 15\; individuals$$

$$Download\; Sample\; Data\; File$$

Step-by-Step R Code to Calculate Correlation and Create Scatter Plot

Step 1 – Define the Data in R

height <- c(150, 152, 155, 158, 160, 162, 165, 168, 170, 172, 175, 178, 180, 183, 185)

weight <- c(48, 50, 52, 54, 56, 58, 60, 62, 64, 65, 68, 70, 72, 75, 78)

Here we are creating two numeric vectors: height and weight.

Step 2 – Calculate Pearson’s Correlation Coefficient

cor.test(height, weight, method = "pearson")

This line performs a Pearson correlation test, which not only calculates the value of r but also gives statistical significance (p-value and confidence interval).

You can extract the r-value and round it for display:

cor_result <- cor.test(height, weight, method = "pearson")

r_value <- round(cor_result$estimate, 2)

Sample Output

Pearson's product-moment correlation

data:  height and weight

t = 35.67, df = 13, p-value = 2.2e-16

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

 0.9871 0.9988

sample estimates:

      cor 

0.99588

This means the correlation is very strong and positive (r ≈ 0.996).

Step 3 – Create a Basic Scatter Plot

plot(height, weight, 

     main = "Height vs Weight", 

     xlab = "Height (cm)", 

     ylab = "Weight (kg)", 

     pch = 19, 

     col = "blue")

This code generates a simple scatter plot with blue circular points.

Step 4 – Add Regression Line

abline(lm(weight ~ height), col = "red")

This line adds a linear regression line in red, showing the trend of the data.

Step 5 – Annotate the Plot with the r Value

text(x = min(height) + 5, y = max(weight) - 2,

     labels = paste("r =", r_value), 

     col = "darkgreen", cex = 1.2, font = 2)

This line places the correlation coefficient (r) on the plot.

correlation-coefficient-scatter-plot-r-studio

Complete Code Block in R Studio

Download Complete correlation coefficient (r) Full R code

Interpretation of Results

Strength and Direction

The calculated r ≈ 0.996 shows a very strong, positive linear relationship between height and weight.

Statistical Significance

The p-value < 0.05 indicates that the correlation is statistically significant.

 Applications of Correlation in Biological Sciences

Domain	Use Case
Epidemiology	Height vs BMI, blood pressure vs cholesterol
Psychology	Stress level vs sleep quality
Environmental Sci.	Temperature vs species diversity
Agriculture	Rainfall vs crop yield

Conclusion

The correlation coefficient (r) is a fundamental statistical tool that reveals relationships between continuous variables. Using R Studio, you can quickly compute this value, test its significance, and visually display it with a scatter plot and regression line.

In our example, height and weight showed a strong positive correlation (r ≈ 0.996), illustrating how R can effectively explore real-world relationships with just a few lines of code.