To calculate the prediction value, you plug in the observed values.

For example, if given an alpha of 2 and a beta of 3, you would calculate the predicted value for an observation whose X is equal to 4 as:

2+3(4)=14

The residual measures the difference between what we observed and what the regression predicted. 

We can move around the equations from above to calculate the residual. 

If we observed a value of 16, then: e = 16-2-3(4) = 2

Note: One common mistake is to subtract the observed from the expected. 

Remember: substantive direction is more important than math. For example:

The prediction is 2 points higher than we observed

=  is the same as =

We observed two points lower than we predict

The regression equation for predicted values is below.

Note: the Regression output is provided for context. Remember that the (e-.05) is scientific notation for "move the decimal place over five spaces to the left."

Expected vote share = 64.07 + .00002047(campaign advertising spending)

To calculate the predicted value for an observation, we would plug in the value of X for said observation or, substantively, how many dollars their campaign spent

Let's say we wanted to look at our prediction for candidate one. We observed that candidate 1 received 69% support.

However, from the equation on the right, we expect that a candidate who spent 100,000 on their election would have the support (or vote) of 66.1% of their party members. 

Therefore, we observed that candidate 1 received 2.9 percent less vote share than we expected, given how much they spent on advertising.