Line of Best Fit

Grade 4

What a line of best fit does

A line of best fit is a straight line drawn through a scatter graph that best represents the trend of the data. You use it to predict values — read across from one axis to find the corresponding value on the other.

The line doesn't have to pass through any specific point, and it certainly doesn't have to start at the origin. It should have roughly the same number of points above it as below it.

Drawing the line

Find the mean of the x-values and the mean of the y-values. Plot that point — your line of best fit should pass through it (or very close to it). Then rotate the line so it balances the cloud of points.

Using the line to predict

EXAMPLE

A line of best fit on a scatter graph shows revision hours (x) vs test score (y). Using the line, estimate the test score for a student who revised for 5 hours.

Find 5 on the x-axis. Draw a vertical line up to the line of best fit. Then draw a horizontal line across to the y-axis and read the value. Suppose it reads 68. Estimated score: 68.

Interpolation vs extrapolation

Interpolation means predicting within the range of the data — this is reliable. Extrapolation means predicting outside the data range — you're extending the line beyond where you have evidence, so the prediction is much less reliable.

If an exam question asks whether a prediction is reliable and it's outside the data range, say it's unreliable because it uses extrapolation. This is a common two-mark question.

Try this one

A sports scientist records the daily temperature (in °C) and the number of cold drinks sold at a leisure centre. The scatter graph is shown below.

(a) Write down the word that best describes the correlation. [1]

Positive Negative No correlation

(b) On a day when the temperature is 22°C, estimate the number of cold drinks sold. [1]

(c) Give one reason why it would not be reliable to use this graph to predict the number of drinks sold on a day when the temperature is 50°C. [1]

Nova's hint:

This question covers scatter graphs, correlation and the reliability of predictions.

For part (b), trace up from 22°C to the trend of the points and read across.

For part (c), ask yourself: 'what would have to be true about the data for a prediction at 50°C to be trustworthy?'

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