Edexcel GCSE Maths Interpreting diagrams
This page covers the following topics:
2. Line of best fit
Scatter graphs can be used to investigate the correlation between the variables they represent. The variables can have a positive, negative or no correlation, depending on the steepness of the pattern the scatter points follow. The two variables that are positively correlated increase together and two variables which are negatively correlated decrease together. Although two variables can be correlated, it does not necessarily mean that the one variable causes the other, as there may be a third one that affects both. Thus, it can be said that correlation does not imply causation.
The line of best fit is a straight line drawn through as many scatter points as possible. Its gradient should generally follow the same steepness of the scatter points. The line of best fit can then be used to make predictions about the values of the variables.
Scatter plots and the lines of best fit through them can be used to make predictions about values of one variable given the other. The stronger the correlation between the two variables, the more accurate the predictions will be.
The line of best fit of a scatter plot can be used for interpolation. Interpolation is the process used to estimate the value of the dependent variable from the independent one without a scatter point for that value. For interpolation to work, the value must lie within the range of the values of the graph.
Extrapolation is the process used to estimate the value of the dependent variable from the independent one without a scatter point for that value for values which are outside the recorded range. Since the values are not within the range, estimates made by extrapolation are less accurate than those made by interpolation.
Can predictions be made for the values of two variables which are very weakly correlated?
The line of best fit between the number of hours spent studying by a student in a week and their percentage grade is given by the equation y = 4x + 18. Explain what this says about the correlation between the two variables.
Describe what you would expect the relationship between the number of ice creams sold and the number of flipflops sold to be.
Find the predicted value of y for when x is 10, given that the equation of the line of best fit for the scatter plot for the two variables is y = 6x + 27.
Using the given scatter plot, find an estimate for the value of y when x is 10.
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