Use a line of best fit to make predictions

A line of best fit models the overall relationship in a scatter plot, allowing a value of one variable to be estimated from a given value of the other using the graph or an associated linear equation. Predictions are approximate because data points vary around the line; interpolation within the observed range is generally more reliable than extrapolation beyond it. Formal regression methods, correlation measures, and uncertainty intervals are not included.

Detailed Explanation: Use a line of best fit to make predictions

A line of best fit shows the overall trend in a scatter plot. It can be used to estimate one variable when the other variable is known.

Worked example

A scatter plot compares the number of hours students study, $x$ , with their test score, $y$ . The data points show a generally increasing trend, so a line of best fit is drawn.

Suppose the equation of the line is

y=6x+52.

Estimate the test score for a student who studies for $6$ hours.

Step 1: Identify the known value

The number of study hours is known:

x=6.

Step 2: Substitute into the line equation

Replace $x$ with $6$ :

y=6(6)+52.

Step 3: Calculate

y=36+52=88.

Step 4: State the prediction

The predicted test score is approximately

\boxed{88}

So, a student who studies for $6$ hours is expected to score about $88$ .

The prediction is approximate because the actual data points do not all lie exactly on the line. A prediction made within the range of study times shown in the scatter plot is usually more reliable than one made far beyond that range.

Learn by doing: Use a line of best fit to make predictions

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Graphing - Scatter Plot (Linear) - Graph to Prediction Given X

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