We want to describe how we can represent the relationship between paired data and use that representation to make predictions. Let's consider a pair of measurement data and a pair of categorical data, one at a time.

Measurement Data

If we have two sets of data that are expressed using numbers, we can show the relationship between them using a scatter plot. Let's consider an example. Suppose that a games shop gathers data about the number of games sold on sale at a particular price.

Price ( $$$ )	$6$	$8$	$9$	$11$	$13$	$14$	$15$	$17$	$18$	$20$
Games Sold	$34$	$28$	$31$	$24$	$20$	$24$	$20$	$14$	$18$	$10$

Both the price and number of games sold are examples of measurement data, so the relationship between them can be presented using a scatter plot.

We can use the scatter plot to make a predictionby using a trend line.

Next, we can find the equation of the trend line. This equation will allow us to predict one data value by using the other corresponding value. For our example, let's assume that the equation of the trend line is as follows.

y = - 1.6 x + 43

If we would like to predict about how many games would be sold for

$ 10,

we could substitute

10

for

x

in the above equation and simplify.

Categorical Data

In the case of a pair of categorical data, we cannot draw a scatter plot. Instead, we can represent the relationship between them using a two-way frequency table. Let's take a look at an example two-way frequency table that presents the relationship between gender and whether that person prefers ebooks or audiobooks.

	Ebooks or Audiobooks?
Gender	Ebook	Audiobook	Total
Male	$22$	$26$	$48$
Female	$27$	$25$	$52$
Total	$49$	$51$	$100$

We can use the table to make a prediction about the type of digital media that a person of a particular gender chooses. To do so, we need to transform our table into a two-way relative frequency table.

	Ebooks or Audiobooks?
Gender	Ebook	Audiobook	Total
Male	$\approx 45 %$	$\approx 51 %$	$48 %$
Female	$\approx 55 %$	$\approx 49 %$	$52 %$
Total	$100 %$	$100 %$	$100 %$

Based on the table, we can predict that females are slightly more likely to choose ebooks than males because $55 % > 45 % .$

Exercise