दिन 31: Correlation और A/B Testing

import pandas as pd
h = pd.read_csv("house_prices.csv")
cols = ["area_sqft", "bedrooms", "age_years", "metro_km", "price_lakh"]
print(h[cols].corr(method="pearson").round(2)["price_lakh"])
print(h[cols].corr(method="spearman").round(2)["price_lakh"])

import numpy as np
import matplotlib.pyplot as plt
rng = np.random.default_rng(1)
x = rng.uniform(-3, 3, 200)
cases = [("r ≈ 0.9", x, 2 * x + rng.normal(0, 1.4, 200)), ("r ≈ −0.6", x, -x + rng.normal(0, 2, 200)),
         ("r ≈ 0 but strong pattern!", x, x ** 2 + rng.normal(0, 0.6, 200))]
fig, ax = plt.subplots(1, 3, figsize=(12, 3.3))
for a, (t, xx, yy) in zip(ax, cases):
    a.scatter(xx, yy, s=8, color="#4f46e5", alpha=0.6); a.set_title(f"{t}  (r={np.corrcoef(xx, yy)[0, 1]:.2f})")
plt.tight_layout(); plt.show()

import pandas as pd
w = pd.read_csv("delhi_weather.csv")
r = w["avg_temp_c"].corr(w["aqi"])
print(f"Temperature vs AQI: r = {r:.2f}")
print("Cold does not create pollution directly: winter brings stubble burning, low wind and")
print("temperature inversion. Temperature is a marker of the season, not the cause.")

from statsmodels.stats.power import NormalIndPower
from statsmodels.stats.proportion import proportion_effectsize
effect = proportion_effectsize(0.13, 0.11)                 # detect 11% → 13%
n = NormalIndPower().solve_power(effect_size=effect, alpha=0.05, power=0.8, ratio=1)
print(f"Need about {n:,.0f} visitors per group ({2 * n:,.0f} total) for 80% power")

import pandas as pd
ab = pd.read_csv("ab_test.csv")
print(ab.head(3))
summary = ab.groupby("group")["converted"].agg(visitors="count", conversions="sum", rate="mean")
summary["rate_%"] = (summary["rate"] * 100).round(2)
print(summary.drop(columns="rate"))
print("Device mix by group (randomisation check):")
print((pd.crosstab(ab["group"], ab["device"], normalize="index") * 100).round(1))

import numpy as np
import pandas as pd
from statsmodels.stats.proportion import proportions_ztest, confint_proportions_2indep
ab = pd.read_csv("ab_test.csv")
g = ab.groupby("group")["converted"].agg(["sum", "count"])
z, p = proportions_ztest(count=[g.loc["B", "sum"], g.loc["A", "sum"]], nobs=[g.loc["B", "count"], g.loc["A", "count"]])
pA, pB = g["sum"] / g["count"]
lo, hi = confint_proportions_2indep(g.loc["B", "sum"], g.loc["B", "count"], g.loc["A", "sum"], g.loc["A", "count"])
print(f"A {pA:.2%} → B {pB:.2%} | absolute lift {pB - pA:+.2%} | relative lift {(pB / pA - 1):+.1%}")
print(f"z = {z:.2f}, p = {p:.4f}")
print(f"95% CI for the lift: {lo:+.2%} to {hi:+.2%}")

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
ab = pd.read_csv("ab_test.csv")
r = ab.groupby(["device", "group"])["converted"].agg(["mean", "count"]).reset_index()
r["se"] = np.sqrt(r["mean"] * (1 - r["mean"]) / r["count"])
fig, ax = plt.subplots(figsize=(8, 3.8))
for i, (grp, c) in enumerate([("A", "#94a3b8"), ("B", "#4f46e5")]):
    d = r[r["group"] == grp]
    ax.bar(np.arange(len(d)) + (i - 0.5) * 0.38, d["mean"] * 100, 0.38, yerr=1.96 * d["se"] * 100, capsize=4, color=c, label=grp)
ax.set_xticks(range(2), r["device"].unique()); ax.set_ylabel("conversion %"); ax.legend(title="checkout")
ax.set_title("New checkout B wins on both devices (95% CI bars)"); plt.show()
print(r.assign(rate_pct=(r["mean"] * 100).round(2))[["device", "group", "count", "rate_pct"]].to_string(index=False))

import pandas as pd
ab = pd.read_csv("ab_test.csv")
rate = ab.groupby("group")["converted"].mean()
visitors, aov = 5_000_000, 1200                      # monthly visitors, average order value ₹
extra_orders = visitors * (rate["B"] - rate["A"])
print(f"Extra orders per month ≈ {extra_orders:,.0f}")
print(f"Extra revenue per month ≈ ₹{extra_orders * aov / 1e7:.1f} crore (point estimate)")