Step by step
The question
Question: find the residual for the line of best fit y = −x + 9 and the point (4, 2).
The point is the real data.
y = −x + 9; (4, 2)
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 = 4 into the line.
It predicts y = 5.
predicted = −(4) + 9 = −4 + 9 = 5
2 Actual minus predicted
Careful!
Not predicted minus actual.
That flips the sign.
Actual comes first.
Careful: not 5 − 2 = 3 ✗
The actual y is 2.
2 minus 5 is −3.
residual = 2 − 5 = −3
So the residual is −3.
It is negative: the point is 3 below 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: 2.
So the answer is right!
5 − 3 = 2
Let's look back.
First: predict.
Then: actual minus predicted.
Last: check.
Answer
residual = 2 − 5 = −3