What Is a Line of Best Fit?
When we collect data involving two variables — like height and shoe size, or hours studied and test score — we often want to see whether there is a pattern or trend. Plotting the data as a scatter graph gives us a visual picture, but we can go further by drawing a line of best fit (also called a regression line) through the data.
A straight line drawn through a scatter plot that best represents the overall trend of the data. It minimises the total distance between the line and all the data points.
The line of best fit allows us to:
- Describe the relationship between two variables
- Predict the value of one variable given the other
- Quantify how strong the linear relationship is
Imagine you're trying to balance a ruler on top of a scattered set of dots — you want to tilt and shift it until it sits as close to as many dots as possible, with roughly equal numbers of dots above and below. That balanced position is essentially what the line of best fit achieves.
Bivariate Data and Scatter Plots
Data that involves two variables collected from the same subject or event. For example, recording both the temperature and ice cream sales on each day gives bivariate data.
Before drawing a line of best fit, we always start by plotting a scatter graph:
- The independent variable (the one we control or choose) goes on the x-axis
- The dependent variable (the one we measure or observe) goes on the y-axis
- Each data point is plotted as a coordinate
Once plotted, we look for correlation — a pattern or relationship between the two variables.
Not all scatter graphs will show a clear linear trend. Before drawing a line of best fit, always check that the data actually follows a roughly linear (straight-line) pattern. Drawing a straight line through data that curves or has no pattern at all is not meaningful.
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