تحليل الارتباط

import pandas as pd
import numpy as np

# students-performance.csv ships with the course — load it from the browser file system.
df = pd.read_csv("students-performance.csv")

# Compute Pearson correlation between two variables
r = df["math score"].corr(df["reading score"], method="pearson")
print(f"Pearson r (math vs reading): {r:.4f}")

rho = df["math score"].corr(df["reading score"], method="spearman")
print(f"Spearman ρ (math vs reading): {rho:.4f}")

# Compare Pearson vs Spearman
pearson = df["math score"].corr(df["reading score"], method="pearson")
spearman = df["math score"].corr(df["reading score"], method="spearman")
print(f"Pearson: {pearson:.4f}  |  Spearman: {spearman:.4f}")

# Full correlation matrix
num_cols = df.select_dtypes(include="number")
corr_matrix = num_cols.corr(method="pearson")
print(corr_matrix.round(3))

import seaborn as sns
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(8, 6))
sns.heatmap(
    corr_matrix,
    annot=True,          # show correlation values
    fmt=".2f",           # two decimal places
    cmap="RdBu_r",       # red-blue diverging colormap
    center=0,            # center colormap at zero
    vmin=-1, vmax=1,     # full correlation range
    square=True,         # square cells
    linewidths=0.5,      # cell borders
    ax=ax
)
ax.set_title("Correlation Matrix — Students Performance")
plt.tight_layout()
plt.show()

import numpy as np

mask = np.triu(np.ones_like(corr_matrix, dtype=bool))

fig, ax = plt.subplots(figsize=(8, 6))
sns.heatmap(
    corr_matrix,
    mask=mask,
    annot=True,
    fmt=".2f",
    cmap="RdBu_r",
    center=0,
    vmin=-1, vmax=1,
    square=True,
    linewidths=0.5,
    ax=ax
)
ax.set_title("Correlation Matrix (Lower Triangle)")
plt.tight_layout()
plt.show()

sns.pairplot(
    df,
    vars=["math score", "reading score", "writing score"],
    hue="gender",
    diag_kind="kde",
    plot_kws={"alpha": 0.4},
    height=3
)
plt.suptitle("Pair Plot: Scores by Gender", y=1.02)
plt.show()

# Check for confounders
# Does the math-reading correlation change after controlling for gender?
for gender in df["gender"].unique():
    subset = df[df["gender"] == gender]
    r = subset["math score"].corr(subset["reading score"])
    print(f"{gender}: math-reading r = {r:.3f}")

# Find highly correlated pairs
high_corr_pairs = []
for i in range(len(corr_matrix.columns)):
    for j in range(i+1, len(corr_matrix.columns)):
        if abs(corr_matrix.iloc[i, j]) > 0.7:
            high_corr_pairs.append((
                corr_matrix.columns[i],
                corr_matrix.columns[j],
                corr_matrix.iloc[i, j]
            ))

print("Highly correlated pairs (|r| > 0.7):")
for col1, col2, r in high_corr_pairs:
    print(f"  {col1} <-> {col2}: r = {r:.3f}")

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

# students-performance.csv ships with the course — load it from the browser file system.
df = pd.read_csv("students-performance.csv")

num_cols = df.select_dtypes(include="number")
corr = num_cols.corr()

# Triangular heatmap
mask = np.triu(np.ones_like(corr, dtype=bool))
fig, ax = plt.subplots(figsize=(8, 6))
sns.heatmap(corr, mask=mask, annot=True, fmt=".2f", cmap="RdBu_r",
            center=0, vmin=-1, vmax=1, square=True, linewidths=0.5, ax=ax)
ax.set_title("Correlation Heatmap")
plt.tight_layout()
plt.show()

# Pair plot
sns.pairplot(df, vars=["math score", "reading score", "writing score"],
             hue="gender", diag_kind="kde", plot_kws={"alpha": 0.4}, height=3)
plt.suptitle("Pair Plot: Scores by Gender", y=1.02)
plt.show()

# Find high correlations
for i in range(len(corr.columns)):
    for j in range(i+1, len(corr.columns)):
        if abs(corr.iloc[i, j]) > 0.5:
            print(f"{corr.columns[i]} <-> {corr.columns[j]}: r = {corr.iloc[i, j]:.3f}")