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CORRELATION To be able to plot scattergraphs accurately To be able to describe and interpret correlation To be able to calculate Sxx, Syy, Sxy and the product moment correlation coefficient (r) To understand the limitation of product moment correlation

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Scattergraphs Vehicles (x) Millions 8.613.412.89.31.39.413.1 Accidents (y) thousands 33513048122346 4.913.59.67.59.823.32119.4 1836503435959969

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Scattergraphs

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Describe and interpret correlation 1st2nd 3rd4th Positive correlation – mainly in the 1 st and 3 rd quadrants Negative correlation – mainly in the 2 nd and 4 th quadrants No correlation – equally spread in all 4 quadrants

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Describe and Interpret Correlation Describe Correlation State whether the correlation is strong or weak, positive, negative or no correlation Interpret Correlation Explain and analyse what the correlation actually means E.g. as an athlete trains for longer their active heartbeat reduces

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Product Moment Correlation Coefficient Calculates the variation between bivariate data Variance = Σ(x – x)², Σ(y – y)², Σ(x – x)(y – y) n n n Sxx = Σ(x – x)² Syy = Σ(y – y)² Sxy = Σ(x – x)(y – y) Notice that variance = Sxx therefore variance x n = Sxx n

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Product Moment Correlation Coefficient Notice that variance = Sxx therefore variance x n = Sxx n Sxx = variance x n Sxx = n Σx² - x ² n Sxx = Σx² - nx ² Sxx = Σx² - n Σx ² n Sxx = Σx² - n Σx ² n² Sxx = Σx² - Σx ² n Syy = Σy² - Σy ² n Sxy = Σxy - ΣxΣy n

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Product Moment Correlation Coefficient r = Sxy Sxx Syy

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VARIANCE Sum of the square of deviation, divided by the total number of observations, is known as Variance. Mathematically, V(x) = δ² = Σ ( x – x )².

VARIANCE Sum of the square of deviation, divided by the total number of observations, is known as Variance. Mathematically, V(x) = δ² = Σ ( x – x )².

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