Step by step
The question
Question: find the residual for the line of best fit y = 4x − 1 and the point (2, 7).
The point is the real data.
y = 4x − 1; (2, 7)
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 = 2 into the line.
It predicts y = 7.
predicted = 4(2) − 1 = 8 − 1 = 7
2 Actual minus predicted
Careful!
Not predicted minus actual.
That flips the sign.
Actual comes first.
Careful: not 7 − 7 = 0 ✗
The actual y is 7.
7 minus 7 is 0.
residual = 7 − 7 = 0
So the residual is 0.
The point is right on the line.
3 Check
Let's check with a picture.
The line of best fit.
The point.
And predicted plus residual gives the actual y: 7.
So the answer is right!
7 + 0 = 7
Let's look back.
First: predict.
Then: actual minus predicted.
Last: check.
Answer
residual = 7 − 7 = 0