Step by step
The question
Question: find the residual for the line of best fit y = 0.5x + 3 and the point (4, 6).
The point is the real data.
y = 0.5x + 3; (4, 6)
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 = 0.5(4) + 3 = 2 + 3 = 5
2 Actual minus predicted
Careful!
Not predicted minus actual.
That flips the sign.
Actual comes first.
Careful: not 5 − 6 = −1 ✗
The actual y is 6.
6 minus 5 is 1.
residual = 6 − 5 = 1
So the residual is 1.
It is positive: the point is 1 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: 6.
So the answer is right!
5 + 1 = 6
Let's look back.
First: predict.
Then: actual minus predicted.
Last: check.
Answer
residual = 6 − 5 = 1