Quick Answer: Correlation in R Result

The R correlation report analyzed 649 rows and 12 numeric variables: G1, G2, G3, age, studytime, failures, absences, Medu, Fedu, traveltime, freetime and goout. The strongest Pearson relationship was between G2 and G3, with r = 0.918548. This is a very strong positive correlation, meaning students with higher second-period grades generally had higher final grades.

The next strongest Pearson correlations were G1 with G2, r = 0.864982, and G1 with G3, r = 0.826387. The strongest negative relationship involving final grade was G3 with failures, r = -0.393316. This means previous failures were moderately associated with lower final grades.

What Is Correlation in R?

Correlation in R means using R to calculate how strongly two numeric variables are associated. The correlation coefficient usually ranges from -1 to +1. A positive coefficient means the variables tend to increase together. A negative coefficient means one variable tends to increase while the other decreases. A coefficient near zero means the linear or rank-based association is weak.

R is excellent for correlation analysis because it has built-in functions for Pearson, Spearman and Kendall correlation. The cor() function calculates correlation matrices, while cor.test() gives a test statistic, p-value and confidence interval for a pair of variables. R can also produce heatmaps, bar charts, scatterplots and report tables.

In this R report, the strongest relationship was G2 with G3. The value r = 0.918548 is very close to +1, so the relationship is very strong and positive. This means students with higher G2 values usually had higher G3 values.

Pearson, Spearman and Kendall Correlation in R

R can calculate different types of correlation depending on the measurement scale and the relationship shape. The R report includes Pearson, Spearman and Kendall heatmaps so that linear, monotonic and ordinal-concordance patterns can be compared.

Pearson Correlation Formula

The Pearson correlation coefficient compares how two variables vary together relative to their own variation. R calculates this directly, but the formula explains the meaning of the value.

If r is positive, the variables move in the same direction. If r is negative, they move in opposite directions. If r is close to zero, the linear association is weak. The p-value tests whether the population correlation is likely to be different from zero.

For the main R result, G2 with G3 produced r = 0.918548 with an extremely small p-value. This means the association is both very strong and statistically significant.

Dataset and Variables Used in R

The R report used the student performance dataset and selected 12 numeric variables. Every selected numeric variable had complete values in the report, and every pairwise correlation used N = 649.

The pairwise sample-size heatmap is important because correlation matrices can be misleading when some cells are based on fewer observations than others. In this R report, all displayed pairwise correlations use the same sample size, so the coefficients are easier to compare.

Verified R Correlation Results

The strongest Pearson relationship in the R report is G2 with G3, with r = 0.918548. This is a very strong positive relationship. The second strongest is G1 with G2, with r = 0.864982. The third strongest is G1 with G3, with r = 0.826387.

The p-values in the report show that the listed top Pearson correlations are statistically significant at alpha .05. The strongest grade correlations also remain important under practical interpretation because their coefficients are large, not merely because their p-values are small.

R Chart-by-Chart Interpretation

The R charts explain the correlation analysis visually. The Pearson heatmap shows the main linear matrix, the Spearman and Kendall heatmaps check rank-based patterns, the strongest-pairs chart ranks the most important relationships, and the sample-size/completeness charts confirm that the matrix is based on stable data coverage.

R Chart 1: Pearson Correlation Heatmap

The Pearson heatmap shows the complete linear correlation matrix. The strongest positive block is around G1, G2 and G3. The cell for G2 with G3 is about 0.92, showing a very strong positive linear relationship. The cells for G1 with G2 and G1 with G3 are also strongly positive.

The heatmap also shows meaningful negative relationships between failures and the grade variables. The relationship between G3 and failures is about -0.39, which is moderate and negative. This chart is the best overall view of the R result because it displays all numeric-variable relationships in one matrix.

R Chart 2: Spearman Correlation Heatmap

The Spearman heatmap measures rank-based monotonic relationships. It confirms the same main pattern as Pearson: G1, G2 and G3 remain the strongest positive cluster. The Spearman value for the G2-G3 relationship is even stronger visually, showing that students who rank high in G2 also tend to rank high in G3.

This chart is useful because it checks whether the Pearson results depend only on linear scale values. Since the Spearman pattern agrees with the Pearson pattern, the conclusion is stronger: grade variables are strongly associated both as raw numeric scores and as rank-order positions.

R Chart 3: Kendall Correlation Heatmap

The Kendall heatmap measures ordinal concordance. Kendall values are usually smaller than Pearson or Spearman values, but the direction and ranking pattern are still consistent. The grade variables remain the strongest positive cluster, while failures remain negatively related to grade outcomes.

This chart supports the reliability of the R result. When Pearson, Spearman and Kendall all point to the same main relationships, the interpretation does not depend on a single correlation method. The final report can confidently say that earlier grades and final grades are strongly associated.

R Chart 4: Strongest Pairwise Relationships

The strongest-pairs chart ranks the largest Pearson correlations. The top positive bar is G2 with G3, followed by G1 with G2 and G1 with G3. These bars show that grade variables dominate the strongest relationships in the dataset.

The chart also includes negative bars for G3 with failures, G2 with failures and G1 with failures. These negative bars are important because they show that previous failures are consistently associated with lower grades. The chart is easier to read than a full heatmap when the goal is to quickly identify the most important relationships.

R Chart 5: Strongest Pair Scatterplot

The scatterplot displays the strongest pair, G2 and G3. The points rise clearly from left to right, and the fitted line has a strong positive slope. This visual pattern matches the Pearson value of r = 0.919. The relationship is not perfect, but it is very strong.

This scatterplot is important because correlation should not be interpreted from a number alone. The graph confirms that the high correlation is visually reasonable and not just a table artifact. It also shows that students with higher G2 scores are generally concentrated at higher G3 scores.

R Chart 6: Pearson and Spearman Agreement

The Pearson-versus-Spearman chart checks whether linear correlations and rank-based correlations lead to similar conclusions. Points near the diagonal line mean both methods agree. In this R report, the main grade relationships remain strong under both methods.

This chart is useful for method validation. If Pearson and Spearman were very different for many pairs, the analysis would need closer inspection for nonlinear relationships or outliers. Here, the agreement supports the use of Pearson as the main report coefficient while still showing that rank-based results tell the same overall story.

R Chart 7: Pairwise Complete Sample Sizes

The pairwise sample-size heatmap shows 649 usable rows for every displayed pair of variables. This is an excellent result because all correlations are based on the same number of observations. When different cells use different sample sizes, the matrix can be harder to compare.

Because every cell uses the same N, the strongest-pairs ranking is easier to trust. The chart confirms that the strongest and weaker correlations are not being compared from uneven sample coverage.

R Chart 8: Numeric Variable Completeness

The numeric-variable completeness chart shows that all selected numeric variables have complete values in the R report. Each bar reaches 100%. This means missing values did not reduce the pairwise correlation sample sizes for the variables shown.

This chart is useful for quality control. Before interpreting a correlation matrix, a researcher should know whether missing data are affecting the analysis. Here, the completeness chart supports the reliability of the R output because all selected variables are fully available.

R Workflow for Correlation Analysis

A complete R correlation workflow should do more than calculate cor(data). It should prepare numeric variables, compute Pearson, Spearman and Kendall matrices, calculate p-values for Pearson pairs, adjust p-values when many pairs are tested, rank the strongest relationships, check pairwise sample sizes and create visual outputs.

Complete R Code Blocks for Correlation in R

1. Load Data and Select Numeric Variables in R

# Correlation in R
# Dataset file should be named dataset.csv in your working directory

df <- read.csv("dataset.csv", stringsAsFactors = FALSE)

numeric_df <- df[sapply(df, is.numeric)]

cat("Number of rows:", nrow(df), "\n")
cat("Number of numeric variables:", ncol(numeric_df), "\n")
print(names(numeric_df))

2. Calculate Pearson, Spearman and Kendall Correlation Matrices

# Pearson correlation matrix
pearson_matrix <- cor(numeric_df, use = "pairwise.complete.obs", method = "pearson")

# Spearman correlation matrix
spearman_matrix <- cor(numeric_df, use = "pairwise.complete.obs", method = "spearman")

# Kendall correlation matrix
kendall_matrix <- cor(numeric_df, use = "pairwise.complete.obs", method = "kendall")

write.csv(round(pearson_matrix, 6), "r_pearson_correlation_matrix.csv")
write.csv(round(spearman_matrix, 6), "r_spearman_correlation_matrix.csv")
write.csv(round(kendall_matrix, 6), "r_kendall_correlation_matrix.csv")

print(round(pearson_matrix, 3))

3. Calculate Pairwise p-values with cor.test()

vars <- names(numeric_df)

results <- data.frame(
  method = character(),
  variable_1 = character(),
  variable_2 = character(),
  n_pairwise = integer(),
  correlation = numeric(),
  absolute_correlation = numeric(),
  p_value = numeric(),
  stringsAsFactors = FALSE
)

for(i in 1:(length(vars) - 1)){
  for(j in (i + 1):length(vars)){
    v1 <- vars[i]
    v2 <- vars[j]

    pair_data <- numeric_df[, c(v1, v2)]
    pair_data <- pair_data[complete.cases(pair_data), ]

    if(nrow(pair_data) >= 3){
      test <- cor.test(pair_data[[v1]], pair_data[[v2]], method = "pearson")

      results <- rbind(results, data.frame(
        method = "pearson",
        variable_1 = v1,
        variable_2 = v2,
        n_pairwise = nrow(pair_data),
        correlation = unname(test$estimate),
        absolute_correlation = abs(unname(test$estimate)),
        p_value = test$p.value
      ))
    }
  }
}

results$p_value_adjusted_bh <- p.adjust(results$p_value, method = "BH")
results <- results[order(-results$absolute_correlation), ]

write.csv(results, "r_pairwise_pearson_results.csv", row.names = FALSE)
head(results, 15)

4. Add Direction, Strength and Decision Labels

strength_label <- function(r){
  ar <- abs(r)
  if(ar >= 0.80) return("Very strong")
  if(ar >= 0.60) return("Strong")
  if(ar >= 0.30) return("Moderate")
  if(ar >= 0.10) return("Weak")
  return("Very weak")
}

results$direction <- ifelse(results$correlation > 0, "Positive",
                            ifelse(results$correlation < 0, "Negative", "Zero"))

results$strength_rule_of_thumb <- sapply(results$correlation, strength_label)

results$decision_alpha_0_05 <- ifelse(results$p_value_adjusted_bh < 0.05,
                                      "Significant", "Not significant")

write.csv(results, "r_pairwise_pearson_results_labeled.csv", row.names = FALSE)

head(results[, c("variable_1", "variable_2", "n_pairwise",
                 "correlation", "p_value_adjusted_bh",
                 "direction", "strength_rule_of_thumb",
                 "decision_alpha_0_05")], 15)

5. Pairwise Complete Sample Size Matrix in R

pairwise_n <- matrix(NA, nrow = length(vars), ncol = length(vars),
                     dimnames = list(vars, vars))

for(i in vars){
  for(j in vars){
    pairwise_n[i, j] <- sum(complete.cases(numeric_df[, c(i, j)]))
  }
}

write.csv(pairwise_n, "r_pairwise_sample_size_matrix.csv")
print(pairwise_n)

6. Variable Completeness Table in R

completeness <- data.frame(
  variable = names(numeric_df),
  complete_values = sapply(numeric_df, function(x) sum(!is.na(x))),
  total_rows = nrow(numeric_df),
  complete_percent = round(sapply(numeric_df, function(x) mean(!is.na(x)) * 100), 2),
  row.names = NULL
)

write.csv(completeness, "r_numeric_variable_completeness.csv", row.names = FALSE)
print(completeness)

7. Run cor.test() for the Strongest Pair

# Strongest pair from this report: G2 with G3
g2_g3_test <- cor.test(numeric_df$G2, numeric_df$G3, method = "pearson")

print(g2_g3_test)

cat("Pearson r:", unname(g2_g3_test$estimate), "\n")
cat("p-value:", g2_g3_test$p.value, "\n")
cat("95% CI:", g2_g3_test$conf.int[1], "to", g2_g3_test$conf.int[2], "\n")

8. Simple R Heatmap Code

png("chart_01_correlation_in_r_pearson_heatmap_colorful.png",
    width = 1400, height = 1100, res = 150)

op <- par(mar = c(8, 8, 5, 2))
image(1:ncol(pearson_matrix), 1:nrow(pearson_matrix),
      t(pearson_matrix[nrow(pearson_matrix):1, ]),
      axes = FALSE,
      col = colorRampPalette(c("#2166ac", "white", "#b2182b"))(100),
      zlim = c(-1, 1),
      xlab = "", ylab = "",
      main = "Correlation in R: Pearson Correlation Heatmap")

axis(1, at = 1:ncol(pearson_matrix), labels = colnames(pearson_matrix), las = 2)
axis(2, at = 1:nrow(pearson_matrix), labels = rev(rownames(pearson_matrix)), las = 2)

for(i in 1:nrow(pearson_matrix)){
  for(j in 1:ncol(pearson_matrix)){
    text(j, nrow(pearson_matrix) - i + 1,
         labels = sprintf("%.2f", pearson_matrix[i, j]),
         cex = 0.7)
  }
}

par(op)
dev.off()

9. R Scatterplot for G2 and G3

plot_data <- numeric_df[complete.cases(numeric_df[, c("G2", "G3")]), c("G2", "G3")]
r_value <- cor(plot_data$G2, plot_data$G3, method = "pearson")

png("chart_05_correlation_in_r_strongest_pair_scatter_colorful.png",
    width = 1200, height = 900, res = 150)

plot(plot_data$G2, plot_data$G3,
     pch = 19,
     col = rgb(0.1, 0.4, 0.8, 0.55),
     main = "Correlation in R: Scatterplot for the Strongest Pair",
     sub = paste0("G2 with G3, Pearson r = ", round(r_value, 3)),
     xlab = "G2",
     ylab = "G3")

abline(lm(G3 ~ G2, data = plot_data), lwd = 3)
grid()

dev.off()

How to Report Correlation in R

When reporting correlation in R, include the method, variables, sample size, coefficient, p-value, confidence interval when available and practical interpretation. The method matters because Pearson, Spearman and Kendall answer related but different questions.

A complete interpretation should also mention that correlation does not prove causation. The R result shows that G2 and G3 move together strongly, but it does not prove that G2 directly causes G3. For modeling work, the strong relationships among G1, G2 and G3 may also require multicollinearity checks and variance inflation factor review.

Common Mistakes in R Correlation

Downloads and Resources for Correlation in R

Use these R output files and images for reviewing the analysis, writing the report and preparing WordPress media.

Official R Documentation

For function details, see the official R documentation for cor() and cor.test().

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