Worked examples
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.
y = 2.5x + 40
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.
fit line: a prediction, points are near 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 = 0: y = 2.5 × 0 + 40 = 0 + 40 = 40
40
x = 1: 2.5 times 1 is 2.5.
Plus 40 is 42.5.
x = 1: y = 2.5 × 1 + 40 = 2.5 + 40 = 42.5
42.5
x = 2: 2.5 times 2 is 5.
Plus 40 is 45.
x = 2: y = 2.5 × 2 + 40 = 5 + 40 = 45
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.
y = 2.5x + 40
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.
Careful: not exactly 2.5 more for everyone ✗
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.
words: 40 + 2.5 + 2.5 + 2.5 = 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!
equation: 2.5 × 3 + 40 = 7.5 + 40 = 47.5
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.
▶ Watch it solved
The question
Question: The line of best fit is y = 2.5x + 40, where x is the number of hours studied and y is the test score.
What does 2.5 mean?
The fit line is y = 2.5x + 40.
We write it big, so we can label it.
y = 2.5x + 40
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.
fit line: a prediction, points are near 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 = 0: y = 2.5 × 0 + 40 = 0 + 40 = 40
40
x = 1: 2.5 times 1 is 2.5.
Plus 40 is 42.5.
x = 1: y = 2.5 × 1 + 40 = 2.5 + 40 = 42.5
42.5
x = 2: 2.5 times 2 is 5.
Plus 40 is 45.
x = 2: y = 2.5 × 2 + 40 = 5 + 40 = 45
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.
y = 2.5x + 40
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.
Careful: not exactly 2.5 more for everyone ✗
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.
words: 40 + 2.5 + 2.5 + 2.5 = 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!
equation: 2.5 × 3 + 40 = 7.5 + 40 = 47.5
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.
▶ Watch it solved
The question
Question: fit line y = −0.5x + 30, x = minutes of waiting, y = happiness score: what does 0.5 mean?
The fit line is y = −0.5x + 30.
We write it big, so we can label it.
y = −0.5x + 30
1 What the letters mean
y is the predicted happiness score.
x is the number of minutes of waiting.
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.
fit line: a prediction, points are near it
2 Make a small table
To see what each number does, we try a few minutes of waiting: 0, 1 and 2.
0 is where it starts.
x = 0: −0.5 times 0 is 0.
Plus 30 is 30.
x = 0: y = −0.5 × 0 + 30 = 0 + 30 = 30
30
x = 1: −0.5 times 1 is −0.5.
Plus 30 is 29.5.
x = 1: y = −0.5 × 1 + 30 = −0.5 + 30 = 29.5
29.5
x = 2: −0.5 times 2 is −1.
Plus 30 is 29.
x = 2: y = −0.5 × 2 + 30 = −1 + 30 = 29
29
Look at the values of y: 30, 29.5, 29.
Each time x goes up 1, y goes down by 0.5.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
y = −0.5x + 30
And 30?
At x = 0, −0.5 times 0 is 0.
Only 30 is left: the first number in the table.
So 30 is the predicted happiness score at 0 minutes of waiting: the start.
Where does minus 0.5 each time come from?
From −0.5x: −0.5 times x.
Each extra minute takes away one more 0.5.
Careful!
The real points are near the line, not on it.
So 0.5 is a predicted change, not an exact one.
Careful: not exactly 0.5 less for everyone ✗
4 Say it in words
So 0.5 means: the predicted happiness score goes down 0.5 for each extra minute.
5 Check
Let's check with x = 3.
In words: start at 30, then take away 0.5 three times.
We get 28.5.
words: 30 − 0.5 − 0.5 − 0.5 = 28.5
The equation with x = 3: −0.5 times 3 is −1.5.
Plus 30 gives 28.5 too.
So the meaning is right!
equation: −0.5 × 3 + 30 = −1.5 + 30 = 28.5
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.
▶ Watch it solved
