Level 5 · Do pricier products sell fewer units?

One point per thing

A scatter plot answers “do two numbers move together?”. Each point is one observation, here one product: its list price across, its units sold up. Build that table first, one row per product:

units = lines.groupby("product_id", as_index=False).agg(units=("quantity", "sum"))
per_product = products[["product_id", "unit_price"]].merge(units, on="product_id")
len(per_product)   # 120 products, all sold at least once

Then draw:

fig, ax = plt.subplots()
ax.scatter(per_product["unit_price"], per_product["units"], alpha=0.6)
ax.set_xlabel("List price (USD)")
ax.set_ylabel("Units sold")

alpha makes the dots partly transparent, so where points pile up you see a darker patch instead of one blob. The pandas version is per_product.plot(kind="scatter", x="unit_price", y="units").

A trend line with np.polyfit

The cloud slopes down, but by how much? np.polyfit(x, y, 1) fits the straight line (degree 1) closest to all the points and returns its slope and intercept:

slope, intercept = np.polyfit(per_product["unit_price"], per_product["units"], 1)
# slope ≈ -0.56, intercept ≈ 608
x = np.array([0, per_product["unit_price"].max()])
ax.plot(x, slope * x + intercept, color="red")

Two x values are enough to draw a straight line. The slope reads in the units of the axes: y units per x unit, so here units sold per dollar of price. -0.56 means that, across the range, each extra $100 of list price goes with about 56 fewer units sold.

Reading it honestly

The best seller, the Delancey Brass Vase at $19.99, sold 2,320 units; the Laurel Teak Solar Lantern at $1,289 sold 6. But the points are widely scattered around the line, so the slope is a summary of the whole range, not a forecast for one product. It also compares different products: it doesn’t say what would happen if Thomas raised the price of one of them. That needs a price test. A scatter shows that two things go together; it doesn’t prove that one causes the other.

Common mistakes

• Plotting every order line instead of one point per product: thousands of overlapping dots.
• Passing y before x to polyfit, which flips the meaning of the slope.
• Reading the slope as cause and effect. It describes how the points lie, nothing more.
• Using ax.plot with markers for a scatter and forgetting linestyle="", which joins the points with lines in table order.