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I have $$-2[\sum_{i=1}^n (y_i*(\bar y)) - \sum_{i=1}^n (y_i*(\bar x)*\frac {S_{(xy)}}{S_{(xx)}})+\sum_{i=1}^n (y_i*x_i*\frac {S_{(xy)}}{S_{(xx)}})]$$

This is a term of a larger sum I am dealing with to derive something in regression. I am allowed to pull out the $y_i$'s in each term because they appear in each sum?

thank you.

the boy 88
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  • MathJax hint: to get multicharacter subscripts, enclose them in braces like the lower sum limit. So S_{(xy)} gives $S_{(xy)}$ – Ross Millikan Sep 17 '17 at 02:59
  • Thank you for that explanation. It was an inquiry myself. – the boy 88 Sep 17 '17 at 03:01
  • That is general in MathJax and LaTeX. Anything in braces is treated as a unit. In a sense, the braces should be required, but the language allows you to remove them around a single character item, which makes $x^2$ much easier to type. – Ross Millikan Sep 17 '17 at 03:05

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In the first two terms you can distribute out the $\sum_{i=1}^ny_i$ because nothing else in the sum depends on $i$. Really you are distributing out the other terms. This does not work in the third term because of the $x_i$.

Ross Millikan
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  • I am sorry, I made a mistake posting the question. Please look at my last edit. – the boy 88 Sep 17 '17 at 03:09
  • I don't see anything in the edit which changes my point. Presumably the $S$s are sums over $xx$ or $xy$ but they could have a different dummy variable, say $j$ – Ross Millikan Sep 17 '17 at 03:16