# GCSE Statistics Chapter 5 Summary- Scatter Diagrams and Correlation

After completing this chapter, you will be able to;

• Draw scatter diagrams
• Recognise correlation
• Know what is meant by a casual relationship
• Draw lines of best fit on scatter diagrams
• Know what is meant by a mean point
• Use lines of best fit to make predictions
• Find the equation of a line of best fit
• Fit a line of best fit to a non-linear model
• Calculate and interpret Spearman’s rank correlation coefficient
• Know what to do with tied ranks.
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Scatter diagrams
1.) If the points on a scatter diagram lie approximately on a straight line, there is
a linear relationship between them. They are associated.
Correlation
2.) Correlation is a measure of the strength of the linear association between
two variables.
3.) Negative correlation is when one variable decreases as the other
increases.
4.) Positive correlation is when one variable increases as the other increases.
5.) Association does not necessarily mean there is linear correlation.
Casual relationships
6.) When a charge in one variable directly causes a change in another variable,
there is a casual relationship between them.
7.) Correlation does not necessarily imply a casual relationship.
Line of best fit
8.) Points on a scatter diagram are strongly correlated if they lie on a straight
line.
9.) A line of best fit is a straight line drawn so that the plotted points on a scatter
diagram are evenly scattered either side of the line.
10.) A line of best fit is a model for the association between the two variables
11.) A line of best fit should pass through the mean point.
12.) Interpolation is when the data point you need lies within the range of the
given values.
13.) Extrapolation is when the data point you need lies outside the range of
values given.
14.) The equation of a line y = ax + b has a gradient a, and its intercept on
the yaxis is (0,b).
15.) The value of the constants in the equation of a line of best fit are calculated
using
a= (y2y1)/(x2x1) and b= y1 ­ ax1 or b=y2 ­ ax2

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Nonlinear models
16.) The graphs of nonlinear models are in the form of y=axn + b
Spearman's rank correlation coefficient
17.) Spearman's rank correlation coefficient is a numerical measure of the
agreement of the correlation between two sets of data. It tells us how close the
agreement is.
18.) Spearman's rank correlation coefficient is given as
rs = 1 (6d2)/(n(n21))
where d is the difference in ranks and n is the number of observations.
Interpretation of Spearman's rank