Step by step
The question
Question: find the residual for the line of best fit y = 2x − 3 and the point (5, 4).
The point is the real data.
y = 2x − 3; (5, 4)
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 = 5 into the line.
It predicts y = 7.
predicted = 2(5) − 3 = 10 − 3 = 7
2 Actual minus predicted
Careful!
Not predicted minus actual.
That flips the sign.
Actual comes first.
Careful: not 7 − 4 = 3 ✗
The actual y is 4.
4 minus 7 is −3.
residual = 4 − 7 = −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: 4.
So the answer is right!
7 − 3 = 4
Let's look back.
First: predict.
Then: actual minus predicted.
Last: check.
Answer
residual = 4 − 7 = −3