Simple
Linear Regression Model

Click below the x axis to get observations.

After you have a few, click on "show reg" to obtain the regression line.

How would you make a prediction for a new y *given*
an x value
?

Click to obtain more observations.

As you add
observations, the regression line changes.

Which is better? The line with fewer observations or with more?

When we make a prediction, what are our sources of error?

We may not have the "right" line !

Even if we have the right line, since the relationship is not exact

there is unpredictable variation about the line.

To address
these issues we need a theoretical model

for how y relates to x.

It has to capture:

A true linear relationship.

An inexact relationship, the points don't fall right on the line.