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LearnEdexcelYMA012018 specificationWST03 · Statistics 3Regression and correlation

WST03 · Module

Regression and correlation

2 subtopics≈ 65 min in total

Start the module: Summary statistics and the PMCC Open graphing calculator

Summary statistics and the PMCC
The summary statistics $S_{xx}$ , $S_{yy}$ and $S_{xy}$ measure spread and how $x$ and $y$ vary together. The product moment correlation coefficient $r=\dfrac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}$ lies between $-1$ and $1$ and measures how close the points are to a straight line.
≈ 30 min
The least squares regression line
The regression line of $y$ on $x$ , $y=a+bx$ , is the straight line that makes the squared vertical distances from the points as small as possible. Its gradient is $b=\dfrac{S_{xy}}{S_{xx}}$ and it always passes through $(\bar x,\bar y)$ , so $a=\bar y-b\bar x$ .
≈ 35 min