Predictions from Data Trends

Predicting what comes next is not only a skill for following a story. When a writer, journalist, or researcher presents a table of numbers or a scatter plot, a careful reader uses the same instinct for anticipation, now applied to numerical evidence rather than plot clues. This lesson extends the reasoning behind Making Predictions into the world of data: instead of using character motivation or foreshadowing, you use the shape of a scatter plot and a line of best fit to anticipate values that were never directly measured.

A scatter plot displays paired data as individual points on a coordinate grid. Before making any prediction, examine how the points are arranged. If the points generally rise from left to right, the data shows a positive correlation: as one quantity increases, so does the other. If the points fall from left to right, the correlation is negative. If the points are scattered with no visible pattern, there is no meaningful correlation, and any prediction drawn from that data would be unreliable.

Consider a small classroom survey comparing hours spent reading per week to scores on a vocabulary quiz. As reading hours increase, quiz scores tend to increase as well, suggesting a positive trend worth investigating further.

A line of best fit is a straight line drawn through a scatter plot so that it sits as close as possible to as many points as possible, with roughly equal numbers of points above and below it. It does not need to touch every point; its purpose is to summarize the overall trend so it can be used for prediction.

Once the line is drawn, pick two points that lie on the line itself (not necessarily original data points) and calculate its slope using \( m = \dfrac{y_2 - y_1}{x_2 - x_1} \). For the reading-and-vocabulary data above, the line passes through approximately \( (1, 60) \) and \( (6, 90) \), giving a slope of \( m = \dfrac{90 - 60}{6 - 1} = 6 \). Using the point \( (1, 60) \), the equation of the line becomes \( y = 6x + 54 \).

This equation is the prediction tool. To predict a quiz score for a student who reads for 3.5 hours a week, substitute \( x = 3.5 \): \( y = 6(3.5) + 54 = 75 \). Because 3.5 hours falls inside the range of the original data (between 1 and 6 hours), this is called interpolation, and it tends to be a fairly reliable prediction.

Predicting a value beyond the range of the collected data is called extrapolation. Using the same equation to predict a score for 8 hours of reading gives \( y = 6(8) + 54 = 102 \). Since no quiz in this data set could score above 100, this result signals that the trend line cannot be extended indefinitely. Real relationships often weaken, level off, or change shape outside the observed range, so extrapolated predictions should always be treated with more caution than interpolated ones.

A careful reader also checks for outliers, single points that sit far from the overall pattern, since these can distort where a line of best fit is drawn and lead to a misleading prediction. Comparing the strength of a trend, how tightly the points cluster around the line, helps you judge how much confidence to place in any prediction made from it. These same judgments about reliability carry forward into Predictions Using Probability, where uncertainty is measured more formally.

Scatter Plot: A graph that displays individual data pairs as points on a coordinate grid to reveal patterns between two variables.

Correlation: The relationship between two variables, described as positive, negative, or absent based on how the data points trend together.

Line of Best Fit: A straight line drawn through a scatter plot to represent the overall trend of the data as closely as possible.

Slope: A measure of how steeply a trend line rises or falls, calculated as the change in the vertical value divided by the change in the horizontal value.

Interpolation: Using a trend line to predict a value that falls within the range of the original data.

Extrapolation: Using a trend line to predict a value beyond the range of the original data, which carries greater uncertainty.

Outlier: A data point that lies noticeably far from the general pattern of the other points.

Making a prediction from a data trend is only half the task; judging whether that prediction is trustworthy is the other half. A strong prediction rests on a clear trend, a reasonable amount of data, and a value that stays within or close to the observed range. A weak prediction relies on scattered data, an extreme outlier, or a value extrapolated far beyond what was ever measured. Recognizing this difference is essential when data trends are used in more advanced contexts, such as Predictions Using Statistical Models, where predictions are refined using more formal mathematical tools.

It is also worth remembering that a strong trend in data shows correlation, not necessarily causation. Two variables can move together without one directly causing the other, so a prediction from a trend line describes a pattern, not a guaranteed explanation.

Related lessons

• Making Predictions