Step by step
The question
Question: find the residual for the line of best fit y = 0.5x + 1 and the point (6, 2).
The point is the real data.
y = 0.5x + 1; (6, 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 = 6 into the line.
It predicts y = 4.
predicted = 0.5(6) + 1 = 3 + 1 = 4
2 Actual minus predicted
Careful!
Not predicted minus actual.
That flips the sign.
Actual comes first.
Careful: not 4 − 2 = 2 ✗
The actual y is 2.
2 minus 4 is −2.
residual = 2 − 4 = −2
So the residual is −2.
It is negative: the point is 2 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!
4 − 2 = 2
Let's look back.
First: predict.
Then: actual minus predicted.
Last: check.
Answer
residual = 2 − 4 = −2