Using the liner model to predict the value of the response

variable for a given value of the explanatory variable is called prediction.

It's as simple as plugging in the value of the x in the

linear model and looking to see what the resulting y, the response variable, is.

According to the following linear model, the model

that we came up with previously, what is

the predicted percentage living in poverty in states

where the high school graduation rate is 82%?

All we need to do to answer this question is to plug

in 82% for the explanatory variable and solve for the predicted response variable.

So we can write our model and simply plug in 82.

Note that we're not plugging in 0.82 here even though we're saying 82%.

Because you can take a look to see what the data looked like.

The high school graduation rate is a value that's between 0 and 100, as opposed

to 0 and 1, as shown by the values on the x-axis of the plot.

Doing a little bit of math, the result comes out to be 13.84%.

So the way we would interpret this number is that, this model predicts that in

states where the high school graduation rate is 82%, the predicted percentage

living in poverty is, on average, 13.84%.

Prediction is a useful and powerful tool, but we want to be careful.

Applying a model estimate to values outside the

realm of the original data is called extrapolation.

In other words, this is simply plugging in a value of the x into

the linear model that was not in the range of the original observed data.

In fact, sometimes the intercept might be an extrapolation as well.

Here, we've stretched out the scatter plot of

the data we've been working with to illustrate this.

Plugging in 0 for the x value into

the linear model will indeed give us the intercept.

But, does it seem like a wise thing to do?

We have no idea if this line actually extends out into infinity as

a straight line, or if it curves down, curves up, or curves down even more.

Any of these are possible.

And since we don't have data from states with such

low high school graduation rates, it's really not wise to believe

the value of the intercept as a plausible value of poverty

rate, if high school graduation rate is 0 for a state.