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Lecture 2

ECON 2209 Lecture 2: 20January_EconStats_karagodsky

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Boston College
ECON 2209

EconStatistics January 20 2017 1 Recap The reordering property is important to know. X3 X j 1 = (X 1 1) + (X2+ 1) + (3 + 1) = (1 + 2 + X3) + (1 + 1 + 1) j=1 We can also separate summations like this 3 X Xt Xt+1= X 1 X 2 X 3 X 4 t=1 Lastly, we can also separate summations like this: 3 3 3 X X X X i Y i Xi+ Yi i=1 i=1 i=1 1.1 Average of the set P 3 i=1 i n this is also called xbar, or the sample average. It will be denoted as such: x i 1.2 Recap of the reordering rules If your friend says that: Xn Xn Xn Xn 2 2 (xiyi+ kxi+ m) = xi yi+ k xi+ nm i=1 i=1 i=1 i=1 Is this true? No! The issue is with separating the rst term. Products of terms with i (nonconstants) must stick together; however k can be factored out because it is a constant. What it should look like is this: X Xn X (x2y + kx + m) = x y + k X + n m i i i ii i i=1 i=1 i=1 1
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