A beginner-friendly introduction to linear regression: understand slope and intercept, see how lines capture relationships in data, and try simple prediction activities using real points and best-fit lines.
The Height Predictor
Meet Mia. She’s 11 years old and growing fast.
Every year, she measures her height and writes it down:
| Age | Height (cm) |
|---|---|
| 8 | 120 |
| 9 | 125 |
| 10 | 130 |
| 11 | 135 |
She plots the points on a graph and connects them — it forms a straight line going up!
Mia looks at the pattern and says,
“If this line keeps going, I’ll be about 140 cm next year!”
She’s just made a prediction — using a line!
Lines Show Relationships
A line is more than a shape — it’s a story about how two things are connected.
In Mia’s case:
- The x-axis is her age.
- The y-axis is her height.
- As one increases, so does the other.
That’s called a positive relationship.
If one goes up while the other goes down, that’s a negative relationship (like “the more you spend, the less money you have left!” 💸).
The Rule of the Line
A line can be written as:
y = m x + b
- m is the slope — how steep the line is (how much it changes each step).
- b is the starting point (where it crosses the y-axis).
Example:
If Mia grows 5 cm each year and started at 120 cm when she was 8, her rule might be:
Height = 5 × (Age − 8) + 120
So when she’s 12:
5 × (12 − 8) + 120 = 140 cm
Math just became a time machine!
Activity 1 — Predict Your Own Future!
- Pick something that grows or changes:
- Your height
- Hours spent reading
- Points scored in a game
- Record it over time.
- Plot it on graph paper or Desmos.
- Draw a line that fits your points.
- Use it to predict the next value!
Bonus: Compare your prediction next week or month — how close were you?
Activity 2 — The Best-Fit Challenge
Give your friends these points:
| x | y |
|---|---|
| 1 | 2 |
| 2 | 5 |
| 3 | 7 |
| 4 | 10 |
| 5 | 13 |
Ask them to draw a line that goes as close to all the points as possible.
Whose line fits best?
That’s what computers do in linear regression — they find the line that fits all the data points perfectly.
How This Connects to Machine Learning
In machine learning, computers use lines (and curves) to make predictions.
- A model predicting your height next year.
- A program estimating tomorrow’s temperature.
- A system guessing what video you’ll watch next.
Each one uses math like:
“If X changes, what will happen to Y?”
That’s exactly what your line did.
So, when you draw a line to predict something — congratulations, you’re doing the same kind of thinking as an AI model!
Takeaway Message
A line isn’t just a picture — it’s a way to predict the future.
Math helps you see where you’ve been and guess what comes next.
Optional Extensions
For Teachers / Parents / Older Students:
- Try graphing two variables that have a negative relationship (like time studying vs. time gaming).
- Use Google Sheets’ “trendline” feature to see real linear regression. See the section below.
- Discuss how errors happen when data doesn’t fit perfectly — just like real life!
Add “trendline” to a chart
- To add a trendlin, select a Chart, right click and select “Edit a Chart”
- At the Chart Editor, select the “Customize” tab
- Find “Series”, and click on the “trendline” checkbox
- You should see a line drawn alone the dots