Step by step
The question
Question: find the residual for the line of best fit y = −2x + 12 and the point (3, 8).
The point is the real data.
y = −2x + 12; (3, 8)
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.
residual = actual − predicted
1 Predict
We put x = 3 into the line.
It predicts y = 6.
predicted = −2(3) + 12 = −6 + 12 = 6
2 Actual minus predicted
Careful!
Not predicted minus actual.
That flips the sign.
Actual comes first.
Careful: not 6 − 8 = −2 ✗
The actual y is 8.
8 minus 6 is 2.
residual = 8 − 6 = 2
So the residual is 2.
It is positive: the point is 2 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!
6 + 2 = 8
Let's look back.
First: predict.
Then: actual minus predicted.
Last: check.
Answer
residual = 8 − 6 = 2