Step by step
The question
Question: find the line of best fit for (1, 5), (2, 7), (3, 1), (4, 0), (5, 0).
The line of best fit is the straight line that comes closest to all the points.
1 Find the means
The mean of the x numbers: 15 divided by 5 is 3.
The mean of the y numbers: 13 divided by 5 is 2.6.
The line of best fit always goes through the mean point, (3, 2.6).
2 Make the table
A table with the points.
Each x minus the mean x, 3.
Each y minus the mean y, 2.6.
For the first point: 1 minus 3 is −2, and 5 minus 2.6 is 2.4.
The product: the two distances multiplied.
−2 times 2.4 is −4.8.
And the x distance squared.
−2 squared is 4.
We add the last two columns: −17 and 10.
3 Find the slope
The slope is the total of the products, over the total of the squares.
Careful!
The bottom uses only the x distances, squared.
Not the y distances.
−17/10 is −1.7.
4 Find b
The line goes through the mean point.
So b is the mean y, minus m times the mean x.
−1.7 times 3 is −5.1.
2.6 minus −5.1 is 7.7.
So the line of best fit is y = −1.7x + 7.7.
5 Draw the line
Now the points on a graph.
Each point is a dot.
The line goes through the mean point.
The line y = −1.7x + 7.7: it passes close to all the points.
6 Check
Let's check: the mean point must be on the line.
−1.7 times 3 plus 7.7 is 2.6.
That is the mean y.
So it is right!
Let's look back.
First: find the means.
Then: make the table.
Then: find the slope.
Then: find b.
Then: draw the line.
Last: check.