How do you describe correlation on a scattergraph, draw a line of best fit, find its equation and use it to estimate values?
Drawing a line of best fit from given data on a scattergraph, describing the type of correlation, finding the equation of the line of best fit, and using it to estimate values.
A focused answer to the SQA National 5 Applications of Mathematics statistics content on scattergraphs, covering describing positive, negative or no correlation, drawing a line of best fit from data, finding the equation of the line in the form y = mx + c, and using it to estimate values.
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What this dot point is asking
The SQA wants you to describe the correlation shown on a scattergraph, draw a line of best fit through the data, find the equation of that line in the form , and use the equation to estimate a value.
Describing correlation
A scattergraph shows whether two quantities are related. The pattern of the points tells you the type and strength of the correlation.
Correlation shows an association between the two quantities, not that one causes the other; this distinction is often worth a mark when interpreting a scattergraph. The strength also matters: points lying very close to a straight line show strong correlation, while points loosely scattered around a trend show weak correlation. A scattergraph with no trend at all, where the points are spread randomly, shows no correlation, and a line of best fit would have little meaning.
Drawing the line of best fit
A line of best fit is a single straight line that follows the trend of the points, drawn so that the points are balanced as evenly as possible on each side. It does not have to pass through any particular point, but it should pass through the middle of the data.
The equation and estimating values
Once the line is drawn, its equation is . The gradient comes from two points on the line, and the intercept is where the line crosses the -axis.
Estimating within the range of the data is reliable; estimating far beyond it is less trustworthy because the trend may not continue. Reading off the graph directly also works for an estimate: go up from the -value to the line, then across to the -axis. The equation simply makes this more precise and lets you estimate values that fall between the gridlines.
Examples in context
Lines of best fit model real relationships: hours studied against exam score, temperature against ice cream sales, a car's age against its value. Drawing the line and reading its equation lets you predict an unknown value, such as the likely score for a given amount of study. The SQA tests describing the correlation, finding the equation and using it to estimate, the skills here.
Try this
Q1. Points on a scattergraph fall from upper left to lower right. Name the correlation. [1 mark]
- Cue. Negative correlation.
Q2. A line of best fit is . Estimate when . [2 marks]
- Cue. .
Q3. A line of best fit passes through and . Find its gradient. [2 marks]
- Cue. .
Exam-style practice questions
Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
SQA N5 Apps style4 marksA line of best fit passes through the points and . Find its equation, then use it to estimate when .Show worked answer →
First find the gradient: (1 mark). The line crosses the -axis at , so the intercept is , giving (1 mark). To estimate when , substitute: (1 mark). Evaluate: (1 mark). Markers reward the gradient, the equation, the substitution, and the estimate.
SQA N5 Apps style2 marksA scattergraph of hours studied against test score shows points rising from lower left to upper right. Describe the correlation and what it means.Show worked answer →
The points rise to the right, so there is positive correlation (1 mark). This means that as the number of hours studied increases, the test score also tends to increase, so more study is associated with higher scores (1 mark). Markers reward naming the correlation as positive and interpreting it in context. Correlation shows an association, not proof that one causes the other.
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