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Use a line of best fit to make predictions

A line of best fit models the overall linear relationship in a scatter plot, representing the trend rather than passing through every data point; its slope and intercept describe how the predicted response changes with the explanatory variable. Learners use the line or its equation to estimate values within the observed data range and cautiously extend predictions just beyond it, distinguishing these estimates from exact values and recognizing that predictions become less reliable farther from the data.

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 does not need to pass through every data point. Use it to make an estimate, not to find an exact value.

Worked example

A scatter plot shows the relationship between the number of hours students study, xx, and their quiz scores, yy. The hours studied range from 11 to 66 hours.

A line of best fit for the data is

y=6x+58y=6x+58

Suppose we want to predict the quiz score for a student who studies for 4.54.5 hours.

Step 1: Identify the explanatory variable.

The number of hours studied is xx, so substitute 4.54.5 for xx.

Step 2: Use the equation.

y=6(4.5)+58y=6(4.5)+58

Step 3: Calculate.

y=27+58=85y=27+58=85

Step 4: State the prediction.

A student who studies for 4.54.5 hours is predicted to score about 85 points.

The word about is important. The line represents the trend, so the actual score could be higher or lower. Since 4.54.5 hours is within the observed range of 11 to 66 hours, this is an interpolation and is generally a reasonable estimate. Predictions much farther beyond the observed range are less reliable.

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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