Step by step
The question
Question: fit line y = 2.5x + 40, x = hours studied, y = test score: what does 2.5 mean?
The fit line is y = 2.5x + 40.
We write it big, so we can label it.
1 What the letters mean
y is the predicted test score.
x is the number of hours studied.
A fit line is drawn through data: real numbers someone collected, shown as points.
The line only predicts: the real points are near it, not on it.
2 Make a small table
To see what each number does, we try a few hours studied: 0, 1 and 2.
0 is where it starts.
x = 0: 2.5 times 0 is 0.
Plus 40 is 40.
x = 1: 2.5 times 1 is 2.5.
Plus 40 is 42.5.
x = 2: 2.5 times 2 is 5.
Plus 40 is 45.
Look at the values of y: 40, 42.5, 45.
Each time x goes up 1, y goes up by 2.5.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 40?
At x = 0, 2.5 times 0 is 0.
Only 40 is left: the first number in the table.
So 40 is the predicted test score at 0 hours studied: the start.
Where does plus 2.5 each time come from?
From 2.5x: 2.5 times x.
Each extra hour adds one more 2.5.
Careful!
The real points are near the line, not on it.
So 2.5 is a predicted change, not an exact one.
4 Say it in words
So 2.5 means: the predicted test score goes up 2.5 for each extra hour.
5 Check
Let's check with x = 3.
In words: start at 40, then add 2.5 three times.
We get 47.5.
The equation with x = 3: 2.5 times 3 is 7.5.
Plus 40 gives 47.5 too.
So the meaning is right!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: say it in words.
Last: check.