Executive Summary

Relationship map across 5 columns

Observations

120

Columns Analysed

5

Pairs Tested

10

Significant Pairs

6

Strongest |r|

0.959

Strongest Pair

Ad Spend ~ Site Visits

Across 120 observations and 10 column pairs, the data is densely interconnected — most metrics move together. The strongest relationship is Ad Spend ~ Site Visits, which move positively together (r = 0.959, p = 2.2e-66). 6 pair(s) are statistically significant at p < 0.05.

Interpretation

The metric landscape is densely interconnected: 6 of 10 pairs show statistically significant movement together (p < 0.05). The strongest relationship is Ad Spend ~ Site Visits (r = 0.959, p = 2.2e-66), a near-perfect positive co-movement. This tight web of associations indicates that most metrics in the dataset are not independent; they rise and fall as part of a few underlying drivers rather than in isolation.

Overview

Analysis Overview

Pairwise Pearson correlations across 5 columns and 120 observations.

N Observations120

N Columns5

N Pairs10

N Significant6

Interpretation

This analysis examines which metrics move together by computing Pearson correlation coefficients—a measure of linear association ranging from -1 (perfect opposition) to +1 (perfect co-movement)—across 5 columns and 120 observations. The 10 possible pairs were tested for statistical significance; 6 of 10 pairs are significant at p < 0.05. Correlation identifies association only; it does not establish causation. The metric r quantifies the strength and direction of paired movements, enabling identification of metrics that rise and fall in tandem or in opposition.

Data Preparation

Data Quality

Column typing, imputation, and exclusions.

Initial Rows120

Final Rows120

Rows Removed0

Interpretation

All 120 rows were retained; no rows were removed during preprocessing. Missing values were imputed using each column's median, ensuring no data loss. All 5 mapped columns (Ad Spend, Site Visits, Orders, Support Tickets, Churn Rate) were usable and included in the correlation analysis. Correlations were computed using pairwise complete observations, preserving the full dataset for relationship detection.

Visualization

Correlation Matrix

Every pairwise correlation across the mapped columns.

Interpretation

Three pairs exhibit strong positive correlation (r ≥ 0.7): Ad Spend ~ Site Visits (0.959), Ad Spend ~ Orders (0.91), and Site Visits ~ Orders (0.91). These form a cohesive block, suggesting they measure related phenomena—traffic and transaction volume scale together with advertising investment. Three pairs show strong negative correlation (r ≤ -0.7): Ad Spend ~ Churn Rate (-0.862), Site Visits ~ Churn Rate (-0.833), and Orders ~ Churn Rate (-0.812). Support Tickets stands apart, showing weak or negligible correlations with all other metrics (range -0.095 to 0.112), indicating it operates independently of the main traffic-and-sales cluster.

Data Table

Strongest Relationships

Top column pairs ranked by absolute correlation, with significance.

Pair	Correlation	P Value	N	Strength	Significance
Ad Spend ~ Site Visits	0.959	2.2e-66	120	strong	***
Ad Spend ~ Orders	0.91	4.77e-47	120	strong	***
Site Visits ~ Orders	0.91	4.99e-47	120	strong	***
Ad Spend ~ Churn Rate	-0.862	1.24e-36	120	strong	***
Site Visits ~ Churn Rate	-0.833	4.05e-32	120	strong	***
Orders ~ Churn Rate	-0.812	2.21e-29	120	strong	***
Support Tickets ~ Churn Rate	0.112	0.222	120	weak
Orders ~ Support Tickets	-0.095	0.304	120	weak
Ad Spend ~ Support Tickets	-0.082	0.374	120	weak
Site Visits ~ Support Tickets	-0.069	0.457	120	weak

Interpretation

The top six relationships all achieve statistical significance (p < 0.001) and strong magnitudes (|r| ≥ 0.81). Ad Spend ~ Site Visits dominates at r = 0.959. Ad Spend ~ Orders and Site Visits ~ Orders tie at r = 0.91. The three Churn Rate pairs—with Ad Spend (-0.862), Site Visits (-0.833), and Orders (-0.812)—reveal a consistent inverse pattern: higher engagement and spending associate with lower churn. The remaining four pairs (Support Tickets with others, p > 0.22) are weak and not statistically reliable, confirming Support Tickets' isolation from the main network.

Visualization

Strongest Pair

The strongest relationship plotted point by point.

Interpretation

The Ad Spend vs Site Visits scatter (r = 0.959) shows a tight linear band across the 120 observations, with Ad Spend ranging from 27.12 to approximately 50+ and Site Visits from 1078 to 2139+. The points cluster closely around an upward trend with minimal scatter, confirming that the high correlation reflects genuine linear co-movement rather than a few extreme outliers. The consistent, tight relationship validates the strength of the r = 0.959 coefficient as a reliable summary of their joint behavior.

Methodology

Statistical methodology and diagnostics for Correlation Analysis

Statistical Method

Correlation Analysis

Standard-library analysis: pairwise correlations across the numeric columns you choose. A full correlation heatmap, the strongest relationships ranked with significance tests, and a scatter of the single strongest pair — so you can see which metrics move together, how tightly, and whether it's statistically real. Works on any dataset: map 2 or more numeric columns.

Data

N = 120 observations

Assumptions

Relationships are approximately linear (Pearson r)
Columns are numeric or cleanly convertible

Limitations

Correlation is not causation
Non-linear or clustered relationships can hide from Pearson r — check the scatter
Outliers can inflate or mask correlations

Software & Citation

MCP Analytics · mcpanalytics.ai

Code Appendix

Analysis Code

Complete R source code for this analysis

Correlation Analysis — What Moves Together

Computes pairwise Pearson correlations across the numeric columns the user selects: full matrix heatmap, strongest relationships ranked with significance tests, and a scatter of the dominant pair.

Why This Method?

Correlation is the fastest map of a dataset's relationships: one number per pair, directly comparable, with a significance test separating real co-movement from noise. It is the standard first step before regression, forecasting, or KPI pruning.

What This Analysis Covers

Full correlation matrix (heatmap)
Strongest relationships ranked with p-values
The dominant pair plotted point by point

Standard Library

Platform standard-library module (LAT-1441): runs on ANY dataset via the semantic mapping {feature_1..feature_N}. All narrative is derived from the user's own column names and computed values.

suppressPackageStartupMessages(library(DT))
suppressPackageStartupMessages(library(htmlwidgets))
suppressPackageStartupMessages(library(arrow))
suppressPackageStartupMessages(library(knitr))
suppressPackageStartupMessages(library(rmarkdown))
suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(tidyr))
suppressPackageStartupMessages(library(ggplot2))
suppressPackageStartupMessages(library(stringr))
suppressPackageStartupMessages(library(lubridate))
suppressPackageStartupMessages(library(broom))
suppressPackageStartupMessages(library(Matrix))
suppressPackageStartupMessages(library(cluster))
suppressPackageStartupMessages(library(data.table))

Core Analysis Pipeline

compute_shared <- function(df, params, col_map = list()) {
  # === SHARED EXPORTS ===
  #   initial_rows/final_rows/rows_removed  $ row accounting
  #   feature_names     $ named character — semantic -> humanized names
  #   used_features     $ character — semantic names used
  #   dropped_features  $ character — excluded columns
  #   cor_long_df       $ data.frame(feature_a, feature_b, correlation) — full matrix
  #   pairs_df          $ data.frame(pair, correlation, p_value, n, strength, significance)
  #   top_pair_df       $ data.frame(value_a, value_b) — <=1000 sample of strongest pair
  #   top_pair_names    $ character(2) — humanized names of the strongest pair
  #   top_r / top_p     $ numeric — strongest pair stats
  #   n_sig             $ integer — pairs significant at p<0.05
  #   metrics / json_output
  # === /SHARED EXPORTS ===

Step 1: Discover mapped features

initial_rows <- nrow(df)
  feat_cols <- grep("^feature_[0-9]+$", names(df), value = TRUE)
  feat_cols <- feat_cols[order(as.integer(sub("^feature_", "", feat_cols)))]
  if (length(feat_cols) < 2) {
    stop("column_mapping must map at least two feature columns(feature_1, feature_2)")
  }
  feature_names <- setNames(humanize_semantic(feat_cols, col_map), feat_cols)

Step 2: Coerce numeric (95% rule); impute median; drop unusable

dropped_features <- character(0)
  for (fc in feat_cols) {
    v <- df[[fc]]
    if (!is.numeric(v)) {
      conv <- suppressWarnings(as.numeric(as.character(v)))
      n_orig <- sum(!is.na(v) & as.character(v) != "")
      if (n_orig > 0 && sum(!is.na(conv)) >= 0.95 * n_orig) {
        df[[fc]] <- conv
      } else {
        dropped_features <- c(dropped_features, fc); next
      }
    }
    v <- df[[fc]]
    med <- median(v, na.rm = TRUE)
    if (is.na(med)) { dropped_features <- c(dropped_features, fc); next }
    v[is.na(v)] <- med
    df[[fc]] <- v
    if (isTRUE(var(v) == 0) || is.na(var(v))) {
      dropped_features <- c(dropped_features, fc)
    }
  }
  used_features <- setdiff(feat_cols, dropped_features)
  if (length(used_features) < 2) {
    stop(paste0("Correlation needs at least two usable numeric columns; only ",
                length(used_features), " remained after cleaning."))
  }
  X <- df[, used_features, drop = FALSE]
  final_rows <- nrow(X)
  rows_removed <- initial_rows - final_rows
  if (final_rows < 10) stop(sprintf("Only %d usable rows — need at least 10.", final_rows))

Step 3: Correlation matrix + per-pair tests

C <- suppressWarnings(cor(X, use = "pairwise.complete.obs", method = "pearson"))
  hn <- unname(feature_names[used_features])

Long format for the heatmap (diagonal included — reads as the standard matrix)

k <- length(used_features)
  cor_long_df <- do.call(rbind, lapply(seq_len(k), function(i) {
    data.frame(feature_a = hn[i], feature_b = hn,
               correlation = round(as.numeric(C[i, ]), 3),
               stringsAsFactors = FALSE)
  }))
  rownames(cor_long_df) <- NULL

Pairwise tests (upper triangle only)

pair_rows <- list()
  for (i in seq_len(k - 1)) {
    for (j in (i + 1):k) {
      r_ij <- C[i, j]
      if (is.na(r_ij)) next
      ct <- tryCatch(cor.test(X[[i]], X[[j]]), error = function(e) NULL)
      p_ij <- if (!is.null(ct)) ct$p.value else NA_real_
      pair_rows[[length(pair_rows) + 1]] <- data.frame(
        pair = paste0(hn[i], " ~ ", hn[j]),
        a = used_features[i], b = used_features[j],
        correlation = round(r_ij, 3),
        p_value = signif(p_ij, 3),
        n = sum(complete.cases(X[[i]], X[[j]])),
        stringsAsFactors = FALSE
      )
    }
  }
  pairs_all <- do.call(rbind, pair_rows)
  if (is.null(pairs_all) || nrow(pairs_all) == 0) {
    stop("No valid correlation pairs could be computed from the mapped columns.")
  }
  pairs_all <- pairs_all[order(-abs(pairs_all$correlation)), , drop = FALSE]
  rownames(pairs_all) <- NULL
  pairs_all$strength <- ifelse(abs(pairs_all$correlation) >= 0.7, "strong",
                        ifelse(abs(pairs_all$correlation) >= 0.4, "moderate", "weak"))
  pairs_all$significance <- ifelse(is.na(pairs_all$p_value), "",
                            ifelse(pairs_all$p_value < 0.001, "***",
                            ifelse(pairs_all$p_value < 0.01, "**",
                            ifelse(pairs_all$p_value < 0.05, "*", ""))))
  n_sig <- sum(pairs_all$p_value < 0.05, na.rm = TRUE)
  pairs_df <- head(pairs_all[, c("pair", "correlation", "p_value", "n",
                                 "strength", "significance")], 15)

Step 4: Strongest pair scatter — <=1000 sample

top <- pairs_all[1, ]
  top_pair_names <- c(feature_names[[top$a]], feature_names[[top$b]])
  set.seed(42)
  sidx <- if (final_rows > 1000) sample(final_rows, 1000) else seq_len(final_rows)
  top_pair_df <- data.frame(
    value_a = X[[top$a]][sidx],
    value_b = X[[top$b]][sidx],
    stringsAsFactors = FALSE
  )
  top_pair_df <- top_pair_df[order(top_pair_df$value_a), ]
  rownames(top_pair_df) <- NULL
  top_r <- top$correlation
  top_p <- top$p_value

  metrics <- list(
    `Observations`        = final_rows,
    `Columns Analysed`    = length(used_features),
    `Pairs Tested`        = nrow(pairs_all),
    `Significant Pairs`   = as.integer(n_sig),
    `Strongest |r|`       = round(abs(top_r), 3),
    `Strongest Pair`      = top$pair
  )

  json_output <- list(
    answer = paste0(
      "Pairwise Pearson correlations on ", length(used_features),
      " columns across ", format(final_rows, big.mark = ","), " rows: ",
      "strongest pair is ", top$pair, " (r = ", top_r,
      if (!is.na(top_p)) paste0(", p = ", top_p) else "", "); ",
      n_sig, " of ", nrow(pairs_all), " pairs significant at p<0.05."
    ),
    cards = lapply(
      c("tldr", "overview", "preprocessing", "correlation_heatmap",
        "strongest_pairs", "top_pair_scatter"),
      function(cid) list(id = cid, metrics = metrics)
    )
  )

  list(
    initial_rows = initial_rows, final_rows = final_rows,
    rows_removed = rows_removed,
    feature_names = feature_names, used_features = used_features,
    dropped_features = dropped_features,
    cor_long_df = cor_long_df, pairs_df = pairs_df, pairs_all = pairs_all,
    top_pair_df = top_pair_df, top_pair_names = top_pair_names,
    top_r = top_r, top_p = top_p, n_sig = n_sig,
    metrics = metrics, json_output = json_output
  )
}

What's wrong with this card?

Executive Summary

Analysis Overview

Data Quality

Correlation Matrix

Strongest Relationships

Strongest Pair

Methodology

Statistical Method

Analysis Code

Correlation Analysis — What Moves Together

Why This Method?

What This Analysis Covers

Standard Library

Core Analysis Pipeline

Step 1: Discover mapped features

Step 2: Coerce numeric (95% rule); impute median; drop unusable

Step 3: Correlation matrix + per-pair tests

Step 4: Strongest pair scatter — <=1000 sample

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