Calculating Predicted Values and Residuals
Calculating Predicted Values
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:
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
Observed vote share for candidate 1
Expected vote share for candidate 1
64.07+.00002047(100000) = 66.1%
Residual vote share for candidate 1
Calculating predicted + residuals
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.