Returned 99 matches (100 formulae, 63 docs)
    Lookup 34.881 ms, Re-ranking 13681.880 ms
    Found 408439 tuple postings, 134996 formulae, 19866 documents
[ formulas ] [ documents ] [ documents-by-formula ]

1.0000
0.0000
75.0000
r x y = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) ( n - 1 ) s x s y = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) i = 1 n ( x i - x ¯ ) 2 i = 1 n ( y i - y ¯ ) 2 ,

0.5704
0.0000
36.0000
k = 1 n ( x k - x ¯ ) ( y k - y ¯ ) k = 1 n ( x k - x ¯ ) 2 k = 1 n ( y k - y ¯ ) 2

0.4426
-16.0000
34.0000
r = r x y = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) i = 1 n ( x i - x ¯ ) 2 i = 1 n ( y i - y ¯ ) 2

0.4228
-14.0000
24.0000
r = i = 1 N ( X i - X ¯ ) ( Y i - Y ¯ ) i = 1 N ( X i - X ¯ ) 2 i = 1 N ( Y i - Y ¯ ) 2

0.3422
-24.0000
20.0000
r ( α , β ) = i ( j i α - j α ¯ ) ( k i β - k β ¯ ) i ( j i α - j α ¯ ) 2 i ( k i β - k β ¯ ) 2 .

0.3257
-37.0000
23.0000
simil ( x , y ) = i I x y ( r x , i - r x ¯ ) ( r y , i - r y ¯ ) i I x y ( r x , i - r x ¯ ) 2 i I x y ( r y , i - r y ¯ ) 2

0.3082
-38.0000
24.0000
= ( n + 1 ) n ( n - 1 ) ( n - 2 ) ( n - 3 ) i = 1 n ( x i - x ¯ ) 4 ( i = 1 n ( x i - x ¯ ) 2 ) 2 - 3 ( n - 1 ) 2 ( n - 2 ) ( n - 3 )

0.2885
-49.0000
21.0000
β ^ = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) i = 1 n ( x i - x ¯ ) 2 = x y ¯ - x ¯ y ¯ x 2 ¯ - x ¯ 2 = Cov [ x , y ] Var [ x ] = r x y s y s x ,

0.2679
-52.0000
18.0000
λ = E ( V ) stdev ( V ) = i = 1 t c i μ i Var ( i = 1 t c i G i ) = i = 1 t c i μ i i = 1 t c i 2 σ i 2 + 2 i = 1 t j = i c i c j σ i j

0.2616
-14.0000
20.0000
b ^ = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) i = 1 n ( x i - x ¯ ) 2 ,

0.2616
-27.0000
18.0000
similarity = cos ( θ ) = A B A B = i = 1 n A i × B i i = 1 n ( A i ) 2 × i = 1 n ( B i ) 2

0.2616
-30.0000
16.0000
β ^ = i = 1 n ( y i - y ¯ ) ( x i - x ¯ ) i = 1 n ( x i - x ¯ ) 2 = C o v ( x , y ) V a r ( x )

0.2275
-26.0000
14.0000
1 = i ( Y i - Y ^ i ) 2 i ( Y i - Y ¯ ) 2 + i ( Y ^ i - Y ¯ ) 2 i ( Y i - Y ¯ ) 2 .

0.2252
-8.0000
16.0000
n ( X ¯ - μ 0 ) i = 1 n ( X i - X ¯ ) 2 / ( n - 1 )

0.2213
-5.0000
17.0000
C n = i = 1 n ( x i - x ¯ n ) ( y i - y ¯ n )

0.2213
-8.0000
13.0000
s x y = 1 N n = 1 N ( x n - x ¯ ) ( y n - y ¯ ) .

0.2213
-12.0000
13.0000
r = 1 n - 1 i = 1 n ( X i - X ¯ ) ( Y i - Y ¯ ) s X s Y

0.2213
-17.0000
13.0000
i = 1 n ( y i - y ¯ ) ( x i - x ¯ ) - β ^ i = 1 n ( x i - x ¯ ) 2 = 0

0.2213
-23.0000
13.0000
β ^ = 1 T t = 1 T ( x t - x ¯ ) ( y t - y ¯ ) 1 T t = 1 T ( x t - x ¯ ) 2 ,

0.2213
-47.0000
17.0000
r x y = x i y i - n x ¯ y ¯ ( n - 1 ) s x s y = n x i y i - x i y i n x i 2 - ( x i ) 2 n y i 2 - ( y i ) 2 .

0.2213
-119.0000
13.0000
i = 1 n 2 ( y ^ i - y ¯ ) ( y i - y ^ i ) = i = 1 n 2 b ^ ( ( y i - y ¯ ) ( x i - x ¯ ) - b ^ ( x i - x ¯ ) 2 ) = 2 b ^ ( i = 1 n ( y i - y ¯ ) ( x i - x ¯ ) - b ^ i = 1 n ( x i - x ¯ ) 2 ) = 2 b ^ i = 1 n ( ( y i - y ¯ ) ( x i - x ¯ ) - ( y i - y ¯ ) ( x i - x ¯ ) ) = 2 b ^ 0 = 0.

0.2140
-10.0000
15.0000
q x y = ( x - x ¯ ) ( y - y ¯ ) I ( x , y ) I ( x , y )

0.2140
-32.0000
15.0000
q x y = ( x - x ¯ ) ( y - y ¯ ) w ( x - x ¯ , y - y ¯ ) I ( x , y ) w ( x - x ¯ , y - y ¯ ) I ( x , y )

0.2140
-37.0000
14.0000
sim ( d j , q ) = 𝐝 𝐣 𝐪 𝐝 𝐣 𝐪 = i = 1 N w i , j w i , q i = 1 N w i , j 2 i = 1 N w i , q 2

0.2116
-31.0000
15.0000
𝐖 = i = 1 n x ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) + i = 1 n y ( 𝐲 i - 𝐲 ¯ ) ( 𝐲 i - 𝐲 ¯ ) n x + n y - 2

0.2079
-23.0000
15.0000
β 1 ^ = ( x i - x ¯ ) ( y i - y ¯ ) ( x i - x ¯ ) 2 and β 0 ^ = y ¯ - β 1 ^ x ¯

0.2062
-74.0000
16.0000
r = i = 1 n i ( j = 1 i n - j + 1 j ) ( [ L ] K d ) i 1 + i = 1 n ( j = 1 i n - j + 1 j ) ( [ L ] K d ) i = i = 1 n i ( n i ) ( [ L ] K d ) i 1 + i = 1 n ( n i ) ( [ L ] K d ) i

0.2005
-18.0000
15.0000
R M D ( S ) = i = 1 n j = 1 n | y i - y j | ( n - 1 ) i = 1 n y i

0.1944
-23.0000
15.0000
S E β ^ = 1 n - 2 i = 1 n ( y i - y ^ i ) 2 i = 1 n ( x i - x ¯ ) 2

0.1944
-38.0000
14.0000
= [ i = 1 N ( x i 2 - x i 1 ) ( x i 2 - x i 1 ) ] - 1 i = 1 N ( x i 2 - x i 1 ) ( y i 2 - y i 1 ) = F D T = 2

0.1944
-50.0000
15.0000
Cov ( X , Y ) = Cov ( X - k x , Y - k y ) = i = 1 n ( x i - K x ) ( y i - K y ) - ( i = 1 n ( x i - K x ) ) ( i = 1 n ( y i - K y ) ) / n n .

0.1927
-14.0000
14.0000
t score = ( β ^ - β 0 ) n - 2 SSR / i = 1 n ( x i - x ¯ ) 2 .

0.1871
-3.0000
14.0000
i = 1 n ( x i - x ¯ ) ( θ - x ¯ ) = 0

0.1871
-6.0000
14.0000
variance = s 2 = i = 1 n ( x i - x ¯ ) 2 n - 1

0.1843
-36.0000
13.0000
σ ^ i = k = 1 n ( x k - x ¯ i ) 2 n - 1 σ ^ i , j = k = 1 n ( x k - x ¯ i ) ( x k - x ¯ j ) n - 1

0.1810
-12.0000
14.0000
r = r x y = x i y i - n x ¯ y ¯ ( n - 1 ) s x s y

0.1810
-31.0000
11.0000
F = i = 1 n ( y i ^ - y ¯ ) 2 / k j = 1 k i = 1 n j ( y i j - y i ^ ) 2 / ( n - k - 1 )

0.1810
-36.0000
12.0000
σ 2 = i = 1 N ( x i - x ¯ ) 2 N and s 2 = N N - 1 σ 2 = N N 2 - N i = 1 N ( x i - x ¯ ) 2 .

0.1791
-11.0000
10.0000
σ 2 = i = 1 N w i ( x i - x ¯ * ) 2 i = 1 N w i

0.1791
-33.0000
12.0000
F = j = 1 k n j ( y ¯ j - y ¯ ) 2 / ( k - 1 ) j = 1 k i = 1 n j ( y i j - y ¯ j ) 2 / ( n - k )

0.1736
-17.0000
13.0000
S x y = 1 2 N 2 i = 1 N j = 1 N ( x i - x j ) ( y i - y j )

0.1705
-10.0000
15.0000
𝐐 𝐧 = 1 n i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T .

0.1705
-11.0000
15.0000
S = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T 𝐑 p × p .

0.1705
-11.0000
15.0000
𝐐 = 1 n - 1 i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T ,

0.1705
-13.0000
14.0000
q j k = 1 N i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k )

0.1705
-16.0000
14.0000
q j k = 1 N - 1 i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k ) ,

0.1705
-22.0000
15.0000
i = 1 n ( x i - μ ) ( x i - μ ) T = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T = S

0.1676
-14.0000
12.0000
s M = i = 1 m x i ; s Σ = i = 1 m ( x i - x ¯ ) 2

0.1655
-67.0000
13.0000
λ 1 = ( y 2 - y 3 ) ( x - x 3 ) + ( x 3 - x 2 ) ( y - y 3 ) det ( T ) = ( y 2 - y 3 ) ( x - x 3 ) + ( x 3 - x 2 ) ( y - y 3 ) ( y 2 - y 3 ) ( x 1 - x 3 ) + ( x 3 - x 2 ) ( y 1 - y 3 ) ,
λ 2 = ( y 3 - y 1 ) ( x - x 3 ) + ( x 1 - x 3 ) ( y - y 3 ) det ( T ) = ( y 3 - y 1 ) ( x - x 3 ) + ( x 1 - x 3 ) ( y - y 3 ) ( y 2 - y 3 ) ( x 1 - x 3 ) + ( x 3 - x 2 ) ( y 1 - y 3 ) ,

0.1600
-23.0000
11.0000
σ y 2 = 1 n i = 1 n ( y i - y ¯ ) 2 = ( 1 n i = 1 n y i 2 ) - y ¯ 2

0.1600
-30.0000
10.0000
K = ( N - 1 ) i = 1 g n i ( r ¯ i - r ¯ ) 2 i = 1 g j = 1 n i ( r i j - r ¯ ) 2 ,

0.1600
-46.0000
11.0000
s 1 = ( x 2 - x 2 ) 2 + ( y 2 - y 1 ) 2 ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 = ( y 2 - y 1 ) 2 ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 ,

0.1568
-25.0000
14.0000
Γ = i , j = 1 n a i j b i j i , j = 1 n a i j 2 i , j = 1 n b i j 2

0.1541
-7.0000
12.0000
s = i = 1 n ( x i - x ¯ ) 2 n - 1

0.1541
-20.0000
12.0000
i = 1 n ( x i - μ ) 2 = i = 1 n ( x i - x ¯ ) 2 + n ( x ¯ - μ ) 2

0.1541
-22.0000
11.0000
s 2 = i = 1 n ( x i - K ) 2 - ( i = 1 n ( x i - K ) ) 2 / n n - 1 .

0.1541
-28.0000
10.0000
SSE = i = 1 n ( X i - X ¯ ) 2 + i = 1 n ( Y i - Y ¯ ) 2 + i = 1 n ( Z i - Z ¯ ) 2

0.1541
-29.0000
12.0000
i = 1 n ( y i - y ¯ ) 2 = i = 1 n ( y i - y ^ i ) 2 + i = 1 n ( y ^ i - y ¯ ) 2 .

0.1541
-32.0000
12.0000
C = μ ^ 4 σ ^ 4 = 1 n i = 1 n ( x i - x ¯ ) 4 ( 1 n i = 1 n ( x i - x ¯ ) 2 ) 2 ,

0.1541
-32.0000
12.0000
s n 2 = 1 n i = 1 n ( x i - x ¯ ) 2 = i = 1 n ( x i 2 ) n - ( i = 1 n x i ) 2 n 2

0.1541
-34.0000
12.0000
V 2 , n = 1 n 2 i = 1 n j = 1 n 1 2 ( x i - x j ) 2 = 1 n i = 1 n ( x i - x ¯ ) 2 ,

0.1541
-34.0000
12.0000
S = μ ^ 3 σ ^ 3 = 1 n i = 1 n ( x i - x ¯ ) 3 ( 1 n i = 1 n ( x i - x ¯ ) 2 ) 3 / 2 ,

0.1541
-35.0000
12.0000
b 1 = m 3 s 3 = 1 n i = 1 n ( x i - x ¯ ) 3 [ 1 n - 1 i = 1 n ( x i - x ¯ ) 2 ] 3 / 2 ,

0.1541
-35.0000
12.0000
g 2 = m 4 m 2 2 - 3 = 1 n i = 1 n ( x i - x ¯ ) 4 ( 1 n i = 1 n ( x i - x ¯ ) 2 ) 2 - 3

0.1541
-36.0000
12.0000
g 1 = m 3 m 2 3 / 2 = 1 n i = 1 n ( x i - x ¯ ) 3 ( 1 n i = 1 n ( x i - x ¯ ) 2 ) 3 / 2 ,

0.1541
-39.0000
12.0000
= ( n + 1 ) n ( n - 1 ) ( n - 2 ) ( n - 3 ) i = 1 n ( x i - x ¯ ) 4 k 2 2 - 3 ( n - 1 ) 2 ( n - 2 ) ( n - 3 )

0.1541
-40.0000
9.0000
s 2 = 1 3 N { n = 1 N ( x n , 1 - x ¯ ) 2 + n = 1 N ( x n , 2 - x ¯ ) 2 + n = 1 N ( x n , 3 - x ¯ ) 2 }

0.1541
-40.0000
9.0000
R 2 = ( y ^ i - y ¯ ) 2 ( y i - y ¯ ) 2 = y T P T L P y y T L y = 1 - y T M y y T L y = 1 - SSR TSS

0.1541
-47.0000
12.0000
s α ^ = s β ^ 1 n i = 1 n x i 2 = 1 n ( n - 2 ) ( j = 1 n ε ^ j 2 ) i = 1 n x i 2 i = 1 n ( x i - x ¯ ) 2

0.1541
-49.0000
12.0000
s 2 = 1 n - 1 i = 1 n ( x i - x ¯ ) 2 = i = 1 n ( x i 2 ) n - 1 - ( i = 1 n x i ) 2 ( n - 1 ) n = ( n n - 1 ) s n 2 .

0.1541
-50.0000
12.0000
i = 1 n ( y i - y ¯ ) 2 = i = 1 n ( y i - y ^ i ) 2 + i = 1 n ( y ^ i - y ¯ ) 2 + i = 1 n 2 ( y ^ i - y ¯ ) ( y i - y ^ i ) .

0.1541
-50.0000
11.0000
1 N i = 1 N ( x i - x ¯ ) 2 = 1 N ( i = 1 N x i 2 ) - x ¯ 2 = ( 1 N i = 1 N x i 2 ) - ( 1 N i = 1 N x i ) 2 .

0.1541
-54.0000
11.0000
S S err = i = 1 N ( y i - y i ^ ) 2 S S tot = i = 1 N ( y i - y ¯ ) 2 S S reg = i = 1 N ( y i ^ - y ¯ ) 2 and y ¯ = 1 N y i i = 1 N .

0.1541
-66.0000
12.0000
F E T = 2 = [ ( x i 1 - x ¯ i ) ( x i 1 - x ¯ i ) + ( x i 2 - x ¯ i ) ( x i 2 - x ¯ i ) ] - 1 [ ( x i 1 - x ¯ i ) ( y i 1 - y ¯ i ) + ( x i 2 - x ¯ i ) ( y i 2 - y ¯ i ) ]

0.1519
-14.0000
11.0000
M D ( S ) = i = 1 n j = 1 n | y i - y j | n ( n - 1 )

0.1519
-20.0000
9.0000
m ^ h ( x ) = i = 1 n K h ( x - x i ) y i i = 1 n K h ( x - x i )

0.1519
-37.0000
11.0000
k ^ - 1 = i = 1 N ( x i k ln x i - x N k ln x N ) i = 1 N ( x i k - x N k ) - 1 N i = 1 N ln x i

0.1519
-39.0000
12.0000
= 2 [ i = 1 N ( x i 2 - x i 1 ) ( x i 2 - x i 1 ) ] - 1 [ i = 1 N 1 2 ( x i 2 - x i 1 ) ( y i 2 - y i 1 ) ]

0.1465
-18.0000
11.0000
var ( r ) = N - n N 1 m x 2 i = 1 n ( y i - r x i ) n - 1

0.1465
-33.0000
10.0000
s 2 = i = 1 N w i ( i = 1 N w i ) 2 - i = 1 N w i 2 . i = 1 N w i ( x i - x ¯ * ) 2

0.1465
-33.0000
7.0000
q y y = ( y - y ¯ ) 2 w ( x - x ¯ , y - y ¯ ) I ( x , y ) w ( x - x ¯ , y - y ¯ ) I ( x , y )

0.1465
-37.0000
10.0000
Σ = i = 1 N w i ( i = 1 N w i ) 2 - i = 1 N w i 2 i = 1 N w i ( 𝐱 i - μ * ) T ( 𝐱 i - μ * ) .

0.1465
-39.0000
10.0000
= w i = 1 N w i ( i = 1 N w i ) 2 - i = 1 N w i 2 . i = 1 N w i . ( x i - x ¯ * ) 2 ( σ x i ) 2

0.1465
-42.0000
10.0000
q j k = i = 1 N w i ( i = 1 N w i ) 2 - i = 1 N w i 2 i = 1 N w i ( x i j - x ¯ j ) ( x i k - x ¯ k ) .

0.1465
-47.0000
10.0000
s 2 = ( x 2 - x 1 ) 2 + ( y 2 - y 2 ) 2 ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 = ( x 2 - x 1 ) 2 ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 .

0.1407
-14.0000
11.0000
μ p q = x y ( x - x ¯ ) p ( y - y ¯ ) q f ( x , y )

0.1407
-15.0000
11.0000
x ¯ = i = 1 n ( x i σ i - 2 ) i = 1 n σ i - 2 ,

0.1407
-17.0000
9.0000
s p 2 = i = 1 k ( n i - 1 ) s i 2 i = 1 k ( n i - 1 )

0.1330
-17.0000
8.0000
η 2 = x n x ( y ¯ x - y ¯ ) 2 x , i ( y x i - y ¯ ) 2

0.1330
-19.0000
7.0000
S 3 = N - 1 i ( x i - x ¯ ) 4 ( N - 1 i ( x i - x ¯ ) 2 ) 2

0.1330
-34.0000
9.0000
q x x = ( x - x ¯ ) 2 w ( x - x ¯ , y - y ¯ ) I ( x , y ) w ( x - x ¯ , y - y ¯ ) I ( x , y )

0.1290
-42.0000
12.0000
1 2 i = 1 n j = 1 n ( x i y j - x j y i ) 2 = i = 1 n x i 2 i = 1 n y i 2 - ( i = 1 n x i y i ) 2 .

0.1272
-11.0000
10.0000
r = y ¯ x ¯ = i = 1 n y i = 1 n x

0.1272
-21.0000
10.0000
r x y = x y ¯ - x ¯ y ¯ ( x 2 ¯ - x ¯ 2 ) ( y 2 ¯ - y ¯ 2 )

0.1272
-66.0000
10.0000
E { ( x ^ - x ) ( y - y ¯ ) T } = E { ( W ( y - y ¯ ) - ( x - x ¯ ) ) ( y - y ¯ ) T } = W E { ( y - y ¯ ) ( y - y ¯ ) T } - E { ( x - x ¯ ) ( y - y ¯ ) T } = W C Y - C X Y .

0.1245
-21.0000
10.0000
μ sig = i = 1 n ( X i - f i ) n μ bkg = i = 1 n ( X i - f i ) n

0.1194
-24.0000
9.0000
R ( M , x ) = x * M x x * x = i = 1 n λ i y i 2 i = 1 n y i 2

0.1150
-34.0000
11.0000
i = 1 n x i γ i i = 1 n ( 1 - x i ) γ i i = 1 n γ i x i i = 1 n γ i ( 1 - x i )

0.0897
-26.0000
10.0000
R n ( ξ , x ) = r 0 x i = 1 n - 1 ( x - x i ) i = 1 n - 1 ( x - x p i )