Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions
A scatter graph shows how two things might be connected. Each point stands for one person or one item, plotted using two measurements at once, like hours of sleep and test score. You already know how to plot a point using an x-value and a y-value. A scatter graph just uses many of those points together to look for a pattern.
Priya asks eight classmates how many hours they revised and what score they got out of 20. She plots each classmate as one point: hours revised on the x-axis, score on the y-axis. Looking at all eight points, she sees them climb upward from left to right. That upward trend is called positive correlation. More revision tends to go with a higher score.
Correlation just describes the pattern in the points. Positive correlation means as one variable goes up, the other tends to go up too, like temperature and ice-cream sales. Negative correlation means as one goes up, the other tends to go down, like the age of a used car and its price. No correlation means there is no clear pattern at all, like shoe size and test scores.
A correlation is not proof of a cause. On a wet day more umbrellas go up and more buses run late, so the two rise together, but no umbrella ever delayed a bus. The rain is doing both. Before you say one thing causes the other, look for a third thing that could be moving them together.
Once the points are plotted you can draw a line of best fit: one straight line through the middle of them, with roughly as many points above as below. It follows the overall trend rather than joining the dots bump by bump. To estimate with it, find your value on one axis, trace across to the line, then read off the other. That works inside the range you plotted; past the ends of your data you cannot tell whether the pattern keeps going.
Points trending up mean positive correlation, points trending down mean negative correlation, scattered points mean no correlation, a line of best fit shows the overall trend, and none of it proves that one thing causes the other.
Last month the two pumpkin beds got one number each, a mean apiece, and the sunny bed's mean was the bigger one. That told Leo and Mia which bed grew better. It never told them why. So this season they wrote down two numbers for every tomato plant on the allotment: hours of sun it gets on a clear day, and kilograms picked off it by October.
The first plant gets 7 hours of sun and gave 4.2 kg. What goes on the graph for it?
Plot the season plant by plant and watch the cloud take a lean. Then try slugs, and shoe sizes.
Jobs that lean on this skill. Follow one to see everything it is built on.
14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.