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Lecture2 -...

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1 Lecture 2. Review of Basic Math, Probability, and Statistics The Summation Operator*** 1 2 1 ... . n i n i x x x x = + + + Basic summation properties: 1 n i c nc = = 1 1 1 1 1 ; ( ) n n n n n i i i i i i i i i i i cx c x x y x y = = = = = = + = + 1 1 1 ( / ) / n n n i i i i i i i x y x y = = = ⎞ ⎛ ⎟ ⎜ ⎠ ⎝ 1 1 2 1 1 ( )( ) ( ) ( ) ( ) n n i i i i i n n i i i i x x y y y y x x x x = = = = , where 1 (1/ ) n i i x n x = = is the sample mean. 1 1 1 1 ( ) 0 n n n n i i i i i i i x x x x x nx nx nx = = = = = = = = 2 2 2 1 1 ( ) ( ) n n i i i i x x x n x = = = 1 1 1 1 ( )( ) ( ) ( ) = . n n n i i i i i i i i i n i i i x x y y x y y x x y x y nxy = = = = = = Linear Functions Y X α β = + The change in Y is always β times the change in X : Y X β Δ = Δ . When 1 (unit) X Δ = , Y β Δ = , so β means how much Y changes when X increases by 1 (unit). So, the marginal effect of X on Y or the slope of X is constant and equals β . The Natural Logarithm
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