A numeric correlation matrix cannot be produced without the underlying data. If you share a dataset containing the four variables (Impressions, CTR, Event Count, Error Rate), I will compute it. Below is a precise, reproducible procedure and code to generate a statistically valid correlation matrix for these variables.
Assumptions and variable mapping
- 曝光 → Impressions (non-negative count)
- 点击率 → CTR in [0, 1]
- 事件数 → Event Count (non-negative count)
- 错误率 → Error Rate in [0, 1]
Methodological notes
- Use transformations to stabilize variance and approximate linearity:
- Counts: log1p(x) = log(1 + x)
- Rates: logit(p) = log(p / (1 − p)); clip to [ε, 1 − ε] to handle 0/1.
- Compute Pearson correlations on transformed variables; optionally compute Spearman correlations for robustness to monotonic nonlinearity and outliers.
- Handle missing/invalid values and filter pathological rows.
- Beware mathematical coupling: CTR is a ratio with Impressions in the denominator, which can induce spurious correlations with Impressions. Interpret correlations involving ratios with caution. If denominators are available, consider weighted correlations or partial correlations controlling for denominators.
Python implementation (pandas, NumPy, SciPy)
- Input: a DataFrame df with columns named exactly as in Chinese or rename as shown.
Code:
import pandas as pd
import numpy as np
from scipy.stats import pearsonr
def logit_series(s, eps=1e-6):
s = s.astype(float).clip(eps, 1 - eps)
return np.log(s / (1 - s))
def build_corr_matrices(df, min_impressions=None):
# Rename to English for clarity (adjust if your column names differ)
rename_map = {'曝光': 'impressions', '点击率': 'ctr', '事件数': 'event_count', '错误率': 'error_rate'}
df = df.rename(columns=rename_map)
cols = ['impressions', 'ctr', 'event_count', 'error_rate']
df = df[cols].apply(pd.to_numeric, errors='coerce')
# Validate ranges and filter
valid = (
(df['impressions'] >= 0) &
(df['event_count'] >= 0) &
(df['ctr'].between(0, 1, inclusive='both')) &
(df['error_rate'].between(0, 1, inclusive='both'))
)
if min_impressions is not None:
valid &= df['impressions'] >= min_impressions
Xraw = df.loc[valid].dropna()
# Transformations
X = pd.DataFrame({
'log1p_impressions': np.log1p(Xraw['impressions']),
'log1p_event_count': np.log1p(Xraw['event_count']),
'logit_ctr': logit_series(Xraw['ctr']),
'logit_error_rate': logit_series(Xraw['error_rate'])
}, index=Xraw.index)
# Pearson correlation on transformed variables
pearson_corr = X.corr(method='pearson')
# Spearman correlation (rank-based, robust to monotonic nonlinearity)
spearman_corr = X.corr(method='spearman')
# Two-sided p-values for Pearson correlations
colsX = X.columns.tolist()
pvals = pd.DataFrame(np.ones((len(colsX), len(colsX))), index=colsX, columns=colsX)
for i, c1 in enumerate(colsX):
for j in range(i + 1, len(colsX)):
c2 = colsX[j]
r, p = pearsonr(X[c1], X[c2])
pvals.loc[c1, c2] = p
pvals.loc[c2, c1] = p
return X, pearson_corr, spearman_corr, pvals
Example usage:
X, pearson_corr, spearman_corr, pvals = build_corr_matrices(df, min_impressions=100)
print(pearson_corr)
print(spearman_corr)
print(pvals)
Interpretation guidance
- The matrices return correlations among:
- log1p_impressions
- log1p_event_count
- logit_ctr
- logit_error_rate
- Positive/negative signs indicate direction of linear association on the transformed scale.
- Check p-values for statistical significance; consider multiple-testing correction if needed.
- Because CTR and Error Rate are ratios, correlation with counts may reflect denominator effects rather than true behavioral associations. Consider:
- Weighted correlation: weight CTR by Impressions and Error Rate by its trial count (if available).
- Partial correlation controlling for Impressions when correlating CTR with other variables.
If you provide a sample of your dataset (or a CSV), I will run this and return the actual correlation matrix.
