Step by step
The question
Question: find the residual for the line of best fit y = 2x + 1 and the point (3, 8).
The point is the real data.
A residual tells how far a point is from the line.
Residual = actual minus predicted.
Actual is the real y.
Predicted is the y the line gives.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Predict
We put x = 3 into the line.
It predicts y = 7.
2 Actual minus predicted
Careful!
Not predicted minus actual.
That flips the sign.
Actual comes first, so a point above the line gets a plus.
The actual y is 8.
8 minus 7 is 1.
So the residual is 1.
It is positive: the point is 1 above the line.
3 Check
Let's check with a picture.
The line of best fit.
The point.
The residual is the distance up or down from the line to the point.
And predicted plus residual gives the actual y: 8.
So the answer is right!
4 Pick the choice
Our answer is residual = 1.
That is choice C.
5 Why not the others
A is −1.
Wrong: predicted minus actual: it is actual minus predicted.
That is the Careful mistake from before.
B is 7.
Wrong: that is the predicted value.
D is 8.
Wrong: that is the actual value.
Let's look back.
First: predict.
Then: actual minus predicted.
Then: check.
Then: pick the choice.
Last: why not the others.