Same Math › Algebra 1 · grades 8–10 › Scatter plots and lines of fit
How do kids read scatter plots and draw a line of fit?
A scatter plot shows pairs of data as dots, like hours studied and test score. If the dots rise left to right, the correlation is positive; if they fall, it's negative; if they're a cloud, there's none. A line of fit runs through the middle of the dots with about half above and half below. Kids write its equation from two points on the line and use it to predict.
- Dots: one for each pair of data.
- Line of fit: follows the trend through the middle.
- Pick two points on the line (not data dots) to write its equation.
Why schools teach it
Turning messy data into a rule
Eighth graders describe patterns in scatter plots and fit straight lines to them by eye (8.SP.A.1 and A.2). In high school they fit lines to data and use them to make predictions (HSS.ID.B.6c), often with a calculator's regression.
The equation of the line is ordinary slope-intercept form. The new idea is that it's an estimate, so two kids' lines can differ a little and both be right.
At the kitchen table
What to say, and what to skip
Say this
As one goes up, what does the other do?
Up, down, or nothing clear?Are there about as many dots above your line as below?
Which two points on your line are easy to read?
Use those for the slope.Does your prediction make sense?
Check it against the dots nearby.
Skip this
- Connecting the dots.A line of fit is one straight line through the middle.
- Forcing the line through the first and last dots.It should balance all the dots.
- Saying correlation proves cause.Ice cream sales and sunburns rise together; summer causes both.
See it in action
A line of fit passes through (2, 60) and (6, 80)
Slope from the two points
(80 − 60) ÷ (6 − 2) = 5Find b
60 = 5(2) + b, so b = 50Predict for x = 8
y = 5(8) + 50 = 90
Slope 5 means each extra hour adds about 5 points.
Free practice sheet
Make a scatter plots sheet
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Parents also ask
What's the difference between a line of fit and a line of best fit?
Best fit usually means the calculator's regression line. A line of fit drawn by eye is close to it.
What's an outlier?
A dot far from the others. Don't let one dot drag the line.
What does r mean on the calculator?
The correlation coefficient: near 1 is strong positive, near −1 strong negative, near 0 none.
What's interpolation versus extrapolation?
Predicting inside the data's range versus beyond it. Beyond is riskier.