Product Moment Correlation Coefficient
Probably a silly question but here goes...
When calculating the Product Moment Correlation Coefficient you need to calculate terms with notation S_xx, S_yy, S_xy (I assume these are the moments?). And in the formula book you see something like this:
S_xx = Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
(Where I've used _ to indicate symbols that are subscripts, ^ to indicate terms that are powers, xbar to indicate x with a bar on top (which is the mean of x) and Sum in place of a big sigma which would indicate a sum over the following terms)
My question is why does:
Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
and not this:
Sum (x_i-xbar)^2 = Sum x_i^2 -2*x_i*x_i/N - (1/N) (Sum x_i)^2
I would have thought there would be a 2*x_i*x_i/N term when you multiply out the bracket.
When calculating the Product Moment Correlation Coefficient you need to calculate terms with notation S_xx, S_yy, S_xy (I assume these are the moments?). And in the formula book you see something like this:
S_xx = Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
(Where I've used _ to indicate symbols that are subscripts, ^ to indicate terms that are powers, xbar to indicate x with a bar on top (which is the mean of x) and Sum in place of a big sigma which would indicate a sum over the following terms)
My question is why does:
Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
and not this:
Sum (x_i-xbar)^2 = Sum x_i^2 -2*x_i*x_i/N - (1/N) (Sum x_i)^2
I would have thought there would be a 2*x_i*x_i/N term when you multiply out the bracket.
Original post by biz2b
Probably a silly question but here goes...
When calculating the Product Moment Correlation Coefficient you need to calculate terms with notation S_xx, S_yy, S_xy (I assume these are the moments?). And in the formula book you see something like this:
S_xx = Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
(Where I've used _ to indicate symbols that are subscripts, ^ to indicate terms that are powers, xbar to indicate x with a bar on top (which is the mean of x) and Sum in place of a big sigma which would indicate a sum over the following terms)
My question is why does:
Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
and not this:
Sum (x_i-xbar)^2 = Sum x_i^2 -2*x_i*x_i/N - (1/N) (Sum x_i)^2
I would have thought there would be a 2*x_i*x_i/N term when you multiply out the bracket.
When calculating the Product Moment Correlation Coefficient you need to calculate terms with notation S_xx, S_yy, S_xy (I assume these are the moments?). And in the formula book you see something like this:
S_xx = Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
(Where I've used _ to indicate symbols that are subscripts, ^ to indicate terms that are powers, xbar to indicate x with a bar on top (which is the mean of x) and Sum in place of a big sigma which would indicate a sum over the following terms)
My question is why does:
Sum (x_i-xbar)^2 = Sum x_i^2 - (1/N) (Sum x_i)^2
and not this:
Sum (x_i-xbar)^2 = Sum x_i^2 -2*x_i*x_i/N - (1/N) (Sum x_i)^2
I would have thought there would be a 2*x_i*x_i/N term when you multiply out the bracket.
I'm too lazy to work out the algebra - it should be online or in a 'decent' stats book - but basically they're doing something like this:
(x - y)^2 = x^2 -2xy + y^2 and then using the fact that x_bar = (sum x)/ n to rewrite the sum.
Is this what you're asking:
?
Unparseable latex formula:
[br]\\[br]\sum (x_i-\bar{x})^2[br]\\[br]=\sum (x_i^2-2x_i\overline{x}+\overline{x}^2)[br]\\[br]=\sum x_i^2-2\overline{x}\sum x_i+n\overline{x}^2[br]\\[br]=\sum x_i^2-2n\overline{x}^2+n\overline{x}^2[br]\\[br]=\sum x_i^2-n\overline{x}^2[br]\\[br]=\sum x_i^2-\sum \overline{x}^2[br]
?
(edited 9 years ago)
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