Covariance_Notes

Covariance_Notes - (7-6 2 =1(3-3 2 =0 4 8(8-6 2 =4(4-3 2 =1...

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Relationship Between Consumption and Income Data Consumption ( i Y ) Income ) ( i X 1 2 2 3 5 10 3 7 4 8 Note: 3 ; 6 ; 6 = = = Y X n (n is the number of pairs of observations) 10.00 8.00 6.00 4.00 2.00 X 5.00 4.00 3.00 2.00 1.00 Y Scatterplot:Consumption (Y) vs. Income (X) Scatterplot shows general upward trend indicating positive relationship. Sample Covariance Between Consumption and Income i Y i X ) ( X X i - ) ( Y Y i - ) )( ( Y Y X X i i - - 1 2 2-6=-4 1-3=-2 -4x-2=8 2 3 3-6=-3 2-3=-1 -3x-1=3 5 10 10-6=4 5-3=2 4x2=8 3 7 7-6=1 3-3=0 1x0=0 4 8 8-6=2 4-3=1 2x1=2 Total 21= = - - n i i i Y Y X X 1 ) )( ( Sample Covariance: = = = - - - = n i i i XY Y Y X X n s 1 25 . 5 4 21 ) )( ( 1 1 Covariance is positive indicating positive relationship.
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Sample Correlation (Coefficient) Between Consumption and Income i Y i X 2 ) ( X X i - 2 ) ( Y Y i - 1 2 (2-6) 2 =16 (1-3) 2 =4 2 3 (3-6) 2 =9 (2-3) 2 =1 5 10 (10-6) 2 =16 (5-3) 2 =4 3 7
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Unformatted text preview: (7-6) 2 =1 (3-3) 2 =0 4 8 (8-6) 2 =4 (4-3) 2 =1 Total 46= ∑-2 ) ( X X i 10= 2 ) ( Y Y i-Sample standard deviation of X: 39116 . 3 4 46 1 ) ( 1 2 = =--= ∑ = n X X s n i i X Sample standard deviation of Y: 58114 . 1 4 10 1 ) ( 1 2 = =--= ∑ = n Y Y s n i i Y Sample covariance between X and Y: 25 . 5 = XY s Correlation coefficient: 979 . ) 58114 . 1 )( 39116 . 3 ( 25 . 5 = = = Y x XY XY s S S r The correlation coefficient is positive indicating a positive relationship. The correlation coefficient is close to +1 indicating a strong positive relationship....
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Covariance_Notes - (7-6 2 =1(3-3 2 =0 4 8(8-6 2 =4(4-3 2 =1...

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