How can a system of equations be used to predict media use?

1 Answer
May 26, 2015

Suppose we have collected data about media use, as follows:

Prnt media:
- year 0 (1994) -> 3 hrs per person per day
- year 1 (1995) -> 2.5 hrs per person per day
- ...

Online media:
- year 0 (1994) -> 0.5 hrs per person per day
- year 1 (1995) -> 0.75 hrs per person per day - ...
- ...

We assume a simple, linear model, so that we can easily fill in the yearly data and we already have sufficient information to determine the equations.

Let's denote by x the number of years passed since 1994 and by y the average number of hours per person per day spent on media use .

Our linear equations will have the general form y=ax+b

For print media use we have:
ax+b = 3 when x = 0 -> b = 3
and ax+b = 2.5 when x=1 -> a+b=2.5 -> a=-0.5
Therefore, our equation for print media use is y = -0.5x+3

For online media use we have:
ax+b=0.5 when x=0 -> b=0.5
and ax+b=0.75 when x=1 -> a+b=0.75 -> a=0.25
Therefore, our equation for online media use is y=0.25x+0.5

Now, we have a system of two linear equations allowing predictions of media use at various data points. (Of course, this is a fictitious example and an oversimplification meant just to illustrate the general idea. We can build a more realistic model by using exponential instead of linear functions).
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