First Charts

Goals

• Prompt an LLM to create a scatter plot and save it to a file.
• Interpret whether a chart answers the question you asked.
• Explain what correlation means and how to read it from a scatter plot.

Why Charts Come First

What is Anscombe's quartet, and why does it matter before we compute any statistics?

• A set of four small datasets with identical means, variances, and correlation [anscombe1973]
  • Their scatter plots look completely different: one is linear, one is curved, one has a single extreme outlier
  • Any statistical summary alone would tell you they are the same; the charts immediately show they are not
• The lesson: look at your data before computing anything
  • A suspicious cluster, a curved pattern, or a handful of extreme points can invalidate a statistical summary
• Charts are not decoration; they are part of the analysis

What dataset will we use, and what question will we ask?

• The dataset for this session is the Natural Resources Canada Earthquake Catalog [nrcan-quakes2025]
  • Download the catalog from NRCan Earthquakes as earthquakes.csv
  • It has one row per recorded earthquake with columns for date, location, depth in kilometres, magnitude, and region
  • Canada experiences thousands of earthquakes per year; most are too small to feel, but British Columbia and Quebec have significant seismic activity
• Do deeper earthquakes tend to have larger magnitudes?
  • Subduction-zone earthquakes (such as those off the BC coast) can be both deep and very large
  • But the relationship is not guaranteed: the chart will show the actual pattern

Drawing the Scatter Plot

Make a scatter plot of earthquake depth on the x axis and magnitude on the y axis, coloured by region, and save it as a PNG.

• The LLM will produce something like:

import polars as pl
import altair as alt

df = pl.read_csv("earthquakes.csv", null_values=[""])
df = df.drop_nulls(subset=["depth", "magnitude", "region"])

chart = (
    alt.Chart(df)
    .mark_point(opacity=0.4, size=20)
    .encode(
        x=alt.X("depth:Q", title="Depth (km)"),
        y=alt.Y("magnitude:Q", title="Magnitude"),
        color=alt.Color("region:N", title="Region"),
        tooltip=["date", "depth", "magnitude", "region"],
    )
    .properties(title="Canadian Earthquakes: Depth vs. Magnitude",
                width=600, height=400)
)
chart.save("scatter.png")
print(f"Points in chart: {len(df)}")

• Run the cell; the file scatter.png appears in the same folder as the notebook
• Open the file to see the chart
  • Most points should cluster at shallow depths and low magnitudes
  • The largest earthquakes may appear at a range of depths, so look for any pattern
  • Different regions (BC, Quebec, Yukon) should appear as distinct colours

Validating the Chart

How do I check that the chart shows all the data I expected?

• Count the rows in the dataframe and compare to the number of points in the chart
  • If the dataframe has 15,000 rows but the chart shows 12,000 points, some data was silently dropped
  • The most common cause is rows with missing values in the columns being plotted
• The code already prints the point count; compare that to the total row count:

import polars as pl

df = pl.read_csv("earthquakes.csv", null_values=[""])
print(f"Total rows in file: {len(df)}")

df_plot = df.drop_nulls(subset=["depth", "magnitude"])
print(f"Rows with both columns present: {len(df_plot)}")
print(f"Rows dropped: {len(df) - len(df_plot)}")

• A large mismatch is worth investigating before drawing conclusions
  • If earthquakes in one region are more likely to have missing depth data, the chart misrepresents that region

Measuring Correlation

Compute the correlation between earthquake depth and magnitude. Drop rows where depth or magnitude is missing.

• The LLM will produce something like:

import polars as pl

df = pl.read_csv("earthquakes.csv", null_values=[""])
df = df.drop_nulls(subset=["depth", "magnitude"])

r = df.select(pl.corr("depth", "magnitude")).item()
print(f"Correlation between depth and magnitude: {r:.3f}")
print(f"(computed from {len(df)} earthquakes with both values present)")

• The output should be a number between -1 and +1
  • A value near 0 means no consistent linear relationship, i.e., deeper quakes are not systematically larger
  • A positive value means deeper quakes tend to be larger; a negative value means the opposite
  • The scatter plot will tell you whether the relationship is linear or curved

What kind of correlation did you calculate?

• Should be Pearson

What does the correlation coefficient actually tell you?

• Correlation measures the strength of a linear relationship between two variables
  • 0.9 is a strong positive relationship; 0.3 is a weak one
  • The number tells you direction and strength, not the slope
• Correlation does not tell you whether one variable causes the other
  • Both earthquake depth and magnitude are determined by tectonic structure, not by each other
  • This distinction matters more in sessions with human data
• A correlation near zero does not mean there is no relationship
  • There may be a non-linear pattern that a linear correlation cannot capture
  • for example, very deep earthquakes in subduction zones tend to be large, while very shallow ones can be large or small

Iterating on Prompts

The chart is hard to read because the points overlap. Adjust the prompt to improve it.

• Prompts rarely produce a perfect chart on the first try
• Common improvements to ask for:
  • "Add transparency (opacity 0.4) so overlapping points are visible."
  • "Remove earthquakes with magnitude below 1.5: they clutter the chart without adding information."
  • "Change the x axis label to 'Depth (km)' and the y axis label to 'Magnitude'."
• After each change, re-run the cell and look at the new PNG
  • If the chart looks worse, describe what changed and ask the LLM to revert that part

Check Understanding

Exercises

Magnitude Distribution

Plot a histogram of earthquake magnitudes. Describe the shape. Are large earthquakes (magnitude 5 or above) common or rare in the catalog?

BC vs. Quebec

Filter the dataset to BC earthquakes and Quebec earthquakes separately. Compute the mean magnitude and mean depth for each. Do the two regions have different seismic characteristics?

Remove Micro-Earthquakes

The catalog includes many micro-earthquakes (magnitude below 2.0) detected only by sensitive instruments. Filter them out and remake the scatter plot. Does the correlation change meaningfully?

Recent Decade

Filter to earthquakes recorded in the last ten years. Is the density of points different from the full catalog? What might explain the difference (hint: think about improvements to monitoring networks)?

Axes in the Wrong Order

The following code draws a scatter plot of depth and magnitude, but the chart looks odd: the x axis runs from 0 to 9 while the label says "Depth (km)." Work with an LLM to find the mismatch and fix it.

import polars as pl
import altair as alt

df = pl.read_csv("earthquakes.csv", null_values=[""])
df = df.drop_nulls(subset=["depth", "magnitude", "region"])

chart = (
    alt.Chart(df)
    .mark_point(opacity=0.4, size=20)
    .encode(
        x=alt.X("magnitude:Q", title="Depth (km)"),
        y=alt.Y("depth:Q", title="Magnitude"),
        color=alt.Color("region:N", title="Region"),
    )
    .properties(title="Canadian Earthquakes: Depth vs. Magnitude",
                width=600, height=400)
)
chart.save("scatter.png")
print(f"Points in chart: {len(df)}")

Chart With No Points on One Axis

The following code draws a scatter plot, but the y axis is empty: all points sit at the bottom of the chart with no visible spread. Work with an LLM to explain why and fix the code.

import polars as pl
import altair as alt

df = pl.read_csv("earthquakes.csv", null_values=[""])
df = df.drop_nulls(subset=["depth", "magnitude"])

chart = (
    alt.Chart(df)
    .mark_point(opacity=0.4, size=20)
    .encode(
        x=alt.X("depth:Q", title="Depth (km)"),
        y=alt.Y("Magnitude:Q", title="Magnitude"),
    )
    .properties(title="Canadian Earthquakes: Depth vs. Magnitude",
                width=600, height=400)
)
chart.save("scatter.png")
print(f"Points in chart: {len(df)}")

Counting Instead of Binning

The following code is meant to plot a histogram of earthquake magnitudes, but every bar is exactly the same height. Work with an LLM to explain why and fix the encoding.

import polars as pl
import altair as alt

df = pl.read_csv("earthquakes.csv", null_values=[""])
df = df.drop_nulls(subset=["magnitude"])

chart = (
    alt.Chart(df)
    .mark_bar()
    .encode(
        x=alt.X("magnitude", title="Magnitude"),
        y=alt.Y("count()", title="Number of Earthquakes"),
    )
    .properties(title="Earthquake Magnitude Distribution",
                width=400, height=300)
)
chart.save("magnitude_hist.png")
print(f"Rows in data: {len(df)}")

Making Dense Points Visible

The following code draws the scatter plot without any transparency, so overlapping points form a solid mass in regions with many earthquakes. Work with an LLM to add opacity so individual points are visible through dense clusters.

import polars as pl
import altair as alt

df = pl.read_csv("earthquakes.csv", null_values=[""])
df = df.drop_nulls(subset=["depth", "magnitude", "region"])

chart = (
    alt.Chart(df)
    .mark_point(size=20)  # TODO: add opacity=0.4 so overlapping points are visible
    .encode(
        x=alt.X("depth:Q", title="Depth (km)"),
        y=alt.Y("magnitude:Q", title="Magnitude"),
        color=alt.Color("region:N", title="Region"),
    )
    .properties(title="Canadian Earthquakes: Depth vs. Magnitude",
                width=600, height=400)
)
chart.save("scatter.png")
print(f"Points in chart: {len(df)}")