CORRELATION To be able to plot scattergraphs accurately
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
Scattergraphs Vehicles (x) Millions 8. 6 13. 4 12. 8 9. 3 1. 3 9. 4 13. 1 Accidents (y) thousands 33 51 30 48 12 23 46 4. 9 13. 5 9. 6 7. 5 9. 8 23. 3 21 19. 4 18 36 50 34 35 95 99 69
Scattergraphs
Describe and interpret correlation 2 nd 1 st 3 rd 4 th 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
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
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 n variance x n = Sxx
Product Moment Correlation Coefficient Notice that variance = Sxx therefore variance x n = Sxx n Sxx = variance x n Sxx = n Σx² - x ² Sxx = Σx² - Σx ² n n Sxx = Σx² - nx ² Sxx = Σx² - n Σx ² n² Syy = Σy² - Σy ² n Sxy = Σxy - ΣxΣy n
Product Moment Correlation Coefficient r= Sxy √Sxx Syy
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