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A Level Mathematics Syllabus Statement

Data presentation and interpretation

Syllabus Content

Interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population (calculations involving regression lines are excluded). Understand informal interpretation of correlation. Understand that correlation does not imply causation

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Here are some exam-style questions on this statement:

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Linear correlation of bivariate data refers to the strength and direction of a linear relationship between two variables. When two variables tend to increase or decrease together in a consistent manner, they are said to have a linear correlation. Pearson’s product-moment correlation coefficient, denoted as \( r \), quantifies the strength and direction of this linear relationship. The value of \( r \) lies between -1 and 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship.

Scatter diagrams, also known as scatter plots, are graphical representations of bivariate data. Each point on the scatter diagram represents a pair of values for the two variables. The pattern of points can give an indication of the type and strength of the relationship between the variables.

The equation of the regression line of \( y \) on \( x \), also known as the least squares regression line, provides a linear model that best fits the data points in a scatter diagram. This line can be used to make predictions about \( y \) based on values of \( x \).

Key formulae [In the exam a GDC would be used to calculate r and to find the equation of the regression line].

$$ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} $$

\( r \) = Pearson’s product-moment correlation coefficient
\( x_i \) and \( y_i \) = Individual data points
\( \bar{x} \) and \( \bar{y} \) = Means of \( x \) and \( y \) respectively

Equation of the regression line of \( y \) on \( x \):

$$ y = a + bx $$

\( b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2} \)
\( a = \bar{y} - b\bar{x} \)

If you use the TI-Nspire calculator you can find instructions for finding the regression line on the GDC Essentials page. The equation of that line can then be used for prediction purposes.

This Bicen Maths video clip shows everything you need to memorise on Regression and Correlation for A Level Statistics.

This video on Bivariate Statistics is from Revision Village and is aimed at students taking the IB Maths AA SL/HL level course.

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