Maths: Analysis and Approaches · Statistics and probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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Bivariate data have two values for each item, plotted as points on a scatter diagram. Pearson's r measures how close the points are to a straight line. It runs from −1 to 1: the sign gives the direction and the size gives the strength. A strong correlation does not prove that one variable causes the other.
A regression line is the line of best fit found by calculation. It always passes through the mean point (x̄, ȳ). The line of y on x is used to estimate y from a given x. The line of x on y is used to estimate x from a given y.
An estimate inside the range of the data is called interpolation. Outside the range it is extrapolation and is unreliable.
Students rearrange the line of y on x to estimate x from a given y. When a separate line of x on y is given, use that line and substitute the y-value straight into it.
Answer: The mean of the y-values is 50.
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