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When you’re examining a set of data, sometimes you’re unsure whether there’s a correlation between two variables or not. When I say correlation, I mean how strong a relationship or connection is there between these two factors. In a scatter plot, we place various points on a graph based on two different variable values, then study the correlation between those variables.
Vocabulary
- Scatter plot: a chart that displays the values of two different variables as points so we can study the correlation between the variables.
- Outliers: data points that don’t fit the general pattern.
Further reading
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When you're examining a set of data,
0:00
sometimes you're unsure whether there's a
correlation between two variables or not.
0:02
When I say correlation,
I mean how strong a relationship or
0:08
connection is there
between these two factors.
0:12
In a scatter plot, we placed various
points on a graph based on two different
0:16
variable values, then study
the correlation between those variables.
0:21
Here's an example of a scatter
plot that compares the temperature
0:28
in Celsius to a store's daily
ice cream sales in dollars.
0:32
As you might expect,
when it's colder than 5 degrees Celsius or
0:36
under about 40 degrees Fahrenheit,
very few people want to eat ice cream.
0:40
Sales don't really pick up until
the thermometer reaches around 25 degrees
0:46
Celsius, which in Fahrenheit
is about the mid to high 70s.
0:50
And from there ice cream
sales really accelerate.
0:54
35 degrees Celsius equals
95 degrees Fahrenheit.
0:57
And on a hot day like that,
you can bet people want ice cream.
1:03
So how do we judge a chart like this?
1:07
I'm looking at the anatomy of a scatter
plot from a website called the data
1:09
visualization catalog.
1:13
The words we would use to describe
the relationship between temperature and
1:16
ice cream sales are positive,
exponential, and strong.
1:20
Positive, because the data
points trend from the lower left
1:25
to the upper right of our chart.
1:29
In other words, as temperature increases,
so do ice cream sales.
1:31
Exponential, because of the shape of
our data forms a curve rather than
1:36
a straight line.
1:40
We don't see a steady increase in ice
cream sales as temperatures rise above
1:42
freezing.
1:46
Rather, we see a small increase in
sales during moderate temperatures and
1:48
a massive leap in sales
once it gets hot out.
1:53
Finally, we say the correlation
between temperature and
1:56
ice cream sales is strong because
there aren't a lot of outliers.
1:59
Outliers are data points that
don't fit the general pattern.
2:04
If for some reason there was
a spike in ice cream sales when
2:09
the temperature was exactly
9 degrees Celsius, and
2:12
sales dipped again at 10 degrees Celsius,
that would be pretty unexpected.
2:16
And the data point would be found
pretty far from our general curve.
2:21
The more outliers in your data,
2:26
the weaker the correlation
between your two variables.
2:28
To look at a basketball example,
2:32
here's a scatter plot comparing NBA win
percentage versus point differential.
2:34
When I say point differential,
2:40
I mean the difference between
points scored and points allowed.
2:42
If your favorite team scores 110
points a game and allows only 100,
2:47
that's a positive 10 point differential,
which is really good.
2:51
According to this chart, a team with
a positive 10 point differential would
2:56
be expected to win 80% of their games.
3:01
The correlation between win percentage and
3:04
point differential is positive,
linear, and strong.
3:07
Teams that outscore their opponents win
games, while teams that don't, lose.
3:11
On the other hand, here's another
chart comparing win percentage to
3:18
points scored. There might be a
positive correlation here, but
3:23
it's an extremely weak one
with lots of outliers. The reason?
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A team needs a strong defense
to win, not just players who can score.
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If your favorite team scores
110 points a game but
3:37
allows 115,
expect them to lose quite a bit.
3:41
A phrase you'll hear often when studying
scatter plots is that correlation
3:46
doesn't equal causation.
3:50
For example, if we were to plot ice
cream sales versus swimsuit sales,
3:53
we'd probably find a positive,
exponential, and strong correlation.
3:58
When ice cream sales are slow,
so are swimsuit sales.
4:03
And when the swimsuit sales pick up,
the same is true for ice cream.
4:07
But does that mean the increase in ice
cream sales caused the increase in
4:12
swimsuit sales?
4:16
Not really.
4:18
People rush to buy both items
because of a third variable,
4:19
an increase in temperature.
4:22
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