Scatter & Line Charts

Maya the bakery owner has a new question. Through one warm fortnight she wrote down, for each of 14 days, the daily high temperature and the number of iced coffees she sold. She suspects hot days sell more iced coffee, but a column of numbers will not tell her. The moment she plots temperature against sales, the answer leans off the page.

In Lesson 1 you learned the grammar: data, an aesthetic mapping inside aes(), and a geom added with +. Now you put it to work with the two geoms you will reach for most.

By the end of this lesson you will be able to:

• Choose geom_point (a scatter) or geom_line for a given question, and say why
• Map a third variable to colour and to size to pack more into one chart
• Add a trend line with geom_smooth() that summarises the whole cloud in one stroke

Prerequisites: Lesson 1, the grammar of graphics (data, aes() mappings, geoms, layering with +). Every new term is defined as it appears.

The scatter: one point per row

A scatterplot answers one precise question: how do two continuous measurements move together? You map one to x, the other to y, and geom_point() draws exactly one dot per row at its (x, y) spot. Fourteen days become fourteen dots, and the shape of the cloud is the relationship.

Each lesson runs in a fresh R session, so build Maya's fortnight right here (run this once):

Now the scatter is the grammar from Lesson 1 with geom_point() as the geom:

The dots climb from lower-left to upper-right: hotter days sold more iced coffee. The widget below reports Pearson's r, a single number from \(-1\) to \(+1\) that measures how tightly the dots hug a straight line (you will study r in depth in correlation analysis; here it just confirms what your eye sees).

The line: a value along an ordered axis

Swap the question. Instead of temperature versus sales, Maya now asks how did sales move across the fortnight? The x axis is no longer a measurement, it is time: day 1, then day 2, then day 3, in order. When x has a natural order, a line is the right geom, because connecting the dots traces the path the value took.

Map day_num to x and add geom_line():

The line walks left to right and you read the journey: a gentle climb with two sharp weekend peaks at days 6, 7 and 13, 14. Toggle the widget between line and point: the same dots, but only the line shows the trajectory from one day to the next.

Which geom fits?

Maya wants to show whether higher foot traffic tends to come with higher revenue, two measurements taken on the same days, with no time order between them. Which geom should she reach for?

A third variable: colour and size

A scatter shows two variables. To pack in a third, map it to another visual channel inside aes(), exactly the move from Lesson 1: anything inside aes() is mapped to a column (and earns a legend); anything outside it is a constant you set by hand.

Map a category to colour and each group gets its own colour. Here day_type (weekday vs weekend) splits the cloud, and you can see the weekend days sit above the weekday trend, hot or not:

Map a continuous column to size and each point swells with its value, a "bubble chart". Here bigger dots are busier days:

Where does it go?

Maya wants each point coloured by day_type so weekends stand out, with a legend telling the reader which colour is which. Which line does that?

Add a trend line

Fourteen dots show a rising relationship, but the eye wants one clean line through the middle to say how fast sales rise with temperature. That is geom_smooth(), added as its own layer on the same data and mapping:

The intuition: the line is the single straight path that sits closest to all the dots at once. The formalism: with method = "lm" it is the least-squares line

\[ \hat{y} = \beta_0 + \beta_1 x \]

where \(x\) is temperature, \(\hat{y}\) (read "y-hat") is the predicted iced-coffee count, \(\beta_0\) (the intercept) is where the line meets the y axis, and \(\beta_1\) (the slope) is how many extra iced coffees each additional degree buys. R picks the \(\beta_0,\beta_1\) that make the total squared vertical gap between dots and line as small as possible:

\[ \min_{\beta_0,\beta_1}\ \sum_{i=1}^{n} \bigl(y_i - \hat{y}_i\bigr)^2 \]

Each \(y_i\) is a day's actual sales, \(\hat{y}_i\) is the line's prediction for that day, and the gap \(y_i-\hat{y}_i\) is the residual. Squaring keeps positives and negatives from cancelling and punishes big misses hardest. Read the exact numbers with lm():

The temp_c coefficient is the slope, about 7: each extra degree of temperature sells roughly seven more iced coffees. The widget shows the same cloud and its Pearson r; geom_smooth() turns that relationship into a line you can read a slope off.

Draw the trend

You have the scatter below. Add a second layer that draws the straight-line (lm) trend through the cloud, with no shaded error band. Fill in the blank.

ggplot(maya, aes(x = temp_c, y = iced_coffees)) +
  geom_point(size = 3) +
  geom_smooth(method = "lm", se = FALSE)

Two traps to dodge

Two mistakes catch almost everyone, and both have a one-line fix.

Overplotting. With many rows, dots land on top of dots and a black blob hides how many points are really there. Make points semi-transparent with alpha (so stacked dots darken) or spread ties apart with geom_jitter():

A line over an unordered x. As you saw, geom_line() only tells the truth when x is ordered. For temperature-versus-sales there is no order to walk along, so stay with geom_point() and add geom_smooth() for the trend, never geom_line().

References

A few authoritative places to take this further:

• ggplot2 reference: geom_point() - every argument of the scatter geom, with overplotting notes (alpha, jitter).
• ggplot2 reference: geom_line() / geom_path() - how line geoms order and connect points, and when to use each.
• ggplot2 reference: geom_smooth() - the trend-line layer, the lm vs loess methods, and the standard-error band.
• R for Data Science (2e): Data visualisation - a gentle hands-on tour of points, lines, colour, size and smooths, with exercises.

Lesson 2 complete

You can now pick the right geom on purpose: geom_point() for the relationship between two continuous variables, geom_line() for one value moving along an ordered axis like time. You mapped a third variable to colour and size to pack more into a single chart, added a least-squares trend line with geom_smooth(method = "lm") and read its slope, and learned to dodge overplotting and the unordered-x line trap.

Next, Lesson 3: Bar and distribution charts. You will use geom_col() and geom_bar() for counts and amounts, and histograms and boxplots to show how a single variable is spread, and learn exactly which question each one answers.