Linear Change of Variance - S1? Watch

george424
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Report Thread starter 7 years ago
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Hello,

I'm revising for my S1 edexcel AS exam, and looking through the specification saw that 'linear change of variance may be required.' This was under the correlation and regression section.

I have never done it, so if anyone could explain it in the context of the unit(correlation and regression) that would be great thanks!

Thanks everyone
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nuodai
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In general, if X is a random variable and a is any number, then \text{Var} (aX + b) = a^2 \text{Var}(X). Also, if X,Y are independent, then \text{Var}(X+Y)= \text{Var}(X) + \text{Var}(Y). [So combining these we get \text{Var}(aX+bY+c) = a^2\text{Var}(X)+b^2\text{Var}(Y  ).]

I'm not sure how much of this is relevant to the S1 syllabus, but provided you know what correlation is and so on, you can work out how this will affect your results. If you're still clueless or if this isn't what you're getting at, then see what your textbook has to say -- if there's nothing there, then you either probably won't need it, or you already know the result without knowing you know it.
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vc94
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Suppose you have 2 variables x and y with correlation coefficient r, then if you apply a linear coding to either x or y, i.e
X= ax +b and Y=cy +d where a,b,c,d are constants then the correlation coeff of X and Y is also r.

For variance there's the result Var(ax + b) = (a^2)Var(x) for any constants a and b.
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george424
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Report Thread starter 7 years ago
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Thanks!

I still don't really get it, but it's not in my textbook so I'll assume we don't need to know it!
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