Returned 99 matches (100 formulae, 64 docs)
    Lookup 696.779 ms, Re-ranking 5570.446 ms
    Found 813116 tuple postings, 162979 formulae, 20880 documents
[ formulas ] [ documents ] [ documents-by-formula ]

1.0000
0.0000
28.0000
k = 1 n ( x k - x ¯ ) ( y k - y ¯ ) k = 1 n ( x k - x ¯ ) 2 k = 1 n ( y k - y ¯ ) 2

1.0000
-32.0000
35.0000
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 ,

0.7176
-15.0000
23.0000
r = i = 1 N ( X i - X ¯ ) ( Y i - Y ¯ ) i = 1 N ( X i - X ¯ ) 2 i = 1 N ( Y i - Y ¯ ) 2

0.7176
-19.0000
25.0000
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

0.5764
-19.0000
19.0000
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 .

0.5474
-34.0000
22.0000
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

0.5404
-38.0000
20.0000
= ( 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 )

0.4116
-16.0000
14.0000
b ^ = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) i = 1 n ( x i - x ¯ ) 2 ,

0.4116
-31.0000
14.0000
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

0.4116
-32.0000
14.0000
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 )

0.4116
-53.0000
14.0000
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 ,

0.3989
-9.0000
13.0000
i = 1 n ( X i - X ¯ ) 2 = X 1 - X ¯ X n - X ¯ 2 .

0.3880
-8.0000
13.0000
S n = 1 n i = 1 n ( X i - X ¯ ) ( X i - X ¯ ) T

0.3880
-8.0000
13.0000
𝐐 𝐧 = 1 n i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T .

0.3880
-8.0000
13.0000
𝐖 = 1 n - 1 i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ )

0.3880
-9.0000
13.0000
S = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T 𝐑 p × p .

0.3880
-9.0000
13.0000
𝐐 = 1 n - 1 i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T ,

0.3880
-9.0000
12.0000
𝐐 = 1 N - 1 i = 1 N ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) T ,

0.3880
-11.0000
13.0000
i = 1 n ( X i - X ¯ ) ( X i - X ¯ ) T W p ( Σ , n - 1 ) .

0.3880
-12.0000
13.0000
r = 1 n - 1 i = 1 n ( X i - X ¯ ) ( Y i - Y ¯ ) s X s Y

0.3880
-14.0000
13.0000
s y m b o l Σ ^ = 1 n i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) T

0.3880
-17.0000
13.0000
s y m b o l Σ ^ = 1 n - 1 i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) T .

0.3880
-17.0000
13.0000
i = 1 n ( y i - y ¯ ) ( x i - x ¯ ) - β ^ i = 1 n ( x i - x ¯ ) 2 = 0

0.3880
-20.0000
13.0000
i = 1 n ( x i - μ ) ( x i - μ ) T = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T = S

0.3880
-22.0000
13.0000
𝐱 ¯ = n - 1 i = 1 n 𝐱 i , 𝐒 = n - 1 i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) .

0.3880
-23.0000
9.0000
β ^ = 1 T t = 1 T ( x t - x ¯ ) ( y t - y ¯ ) 1 T t = 1 T ( x t - x ¯ ) 2 ,

0.3516
-4.0000
10.0000
𝐂 = i = 1 n ( 𝐱 𝐢 - 𝐱 ¯ ) ( 𝐱 𝐢 - 𝐱 ¯ ) T

0.3409
-7.0000
10.0000
Σ b = 1 C i = 1 C ( μ i - μ ) ( μ i - μ ) T

0.3396
-8.0000
16.0000
n ( X ¯ - μ 0 ) i = 1 n ( X i - X ¯ ) 2 / ( n - 1 )

0.3379
-14.0000
13.0000
t score = ( β ^ - β 0 ) n - 2 SSR / i = 1 n ( x i - x ¯ ) 2 .

0.3280
-3.0000
12.0000
i = 1 n ( x i - x ¯ ) ( θ - x ¯ ) = 0

0.3280
-5.0000
12.0000
σ 2 = i = 1 n ( x i - x ¯ ) 2 / ( n - 1 )

0.3173
-19.0000
10.0000
ρ i j ( a i j - a ¯ ) ( a j i - a ¯ ) i j ( a i j - a ¯ ) 2

0.3173
-24.0000
12.0000
S E β ^ = 1 n - 2 i = 1 n ( y i - y ^ i ) 2 i = 1 n ( x i - x ¯ ) 2

0.3173
-25.0000
10.0000
β 1 ^ = ( x i - x ¯ ) ( y i - y ¯ ) ( x i - x ¯ ) 2 and β 0 ^ = y ¯ - β 1 ^ x ¯

0.3074
-34.0000
11.0000
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

0.3043
-20.0000
11.0000
σ y 2 = 1 n i = 1 n ( y i - y ¯ ) 2 = ( 1 n i = 1 n y i 2 ) - y ¯ 2

0.2938
-14.0000
10.0000
s M = i = 1 m x i ; s Σ = i = 1 m ( x i - x ¯ ) 2

0.2830
-5.0000
13.0000
C n = i = 1 n ( x i - x ¯ n ) ( y i - y ¯ n )

0.2830
-11.0000
12.0000
q j k = 1 N i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k )

0.2830
-13.0000
12.0000
q j k = 1 N - 1 i = 1 N ( X i j - X ¯ j ) ( X i k - X ¯ k )

0.2830
-14.0000
12.0000
q j k = 1 N - 1 i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k ) ,

0.2807
-17.0000
11.0000
s 2 = i = 1 n ( x i - K ) 2 - ( i = 1 n ( x i - K ) ) 2 / n n - 1 .

0.2750
-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 )

0.2750
-42.0000
12.0000
S S A B ( i j Y i j ( Y ¯ i - Y ¯ ) ( Y ¯ j - Y ¯ ) ) 2 i ( Y ¯ i - Y ¯ ) 2 j ( Y ¯ j - Y ¯ ) 2

0.2702
0.0000
10.0000
i = 1 n ( X i - X ¯ ) 2
i = 1 n ( y i - y ¯ ) 2

0.2702
-3.0000
10.0000
i = 1 n ( X i - X ¯ ) 2 σ 2

0.2702
-7.0000
10.0000
s = i = 1 n ( x i - x ¯ ) 2 n - 1

0.2702
-7.0000
10.0000
σ X 2 = i = 1 n ( X i - X ¯ ) 2 n .

0.2702
-9.0000
10.0000
variance = s 2 = i = 1 n ( x i - x ¯ ) 2 n - 1

0.2702
-15.0000
8.0000
q x y = ( x - x ¯ ) ( y - y ¯ ) I ( x , y ) I ( x , y )

0.2702
-19.0000
10.0000
1 n i = 1 n ( X i - X ¯ ) 2 < 1 n i = 1 n ( X i - μ ) 2 ,

0.2702
-20.0000
10.0000
i = 1 n ( x i - μ ) 2 = i = 1 n ( x i - x ¯ ) 2 + n ( x ¯ - μ ) 2

0.2702
-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

0.2702
-29.0000
10.0000
i = 1 n ( y i - y ¯ ) 2 = i = 1 n ( y i - y ^ i ) 2 + i = 1 n ( y ^ i - y ¯ ) 2 .

0.2702
-32.0000
10.0000
C = μ ^ 4 σ ^ 4 = 1 n i = 1 n ( x i - x ¯ ) 4 ( 1 n i = 1 n ( x i - x ¯ ) 2 ) 2 ,

0.2702
-32.0000
10.0000
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

0.2702
-39.0000
10.0000
= ( 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 )

0.2702
-50.0000
10.0000
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 ) .

0.2570
-4.0000
8.0000
( x i - x ¯ ) T Σ - 1 ( x i - x ¯ )

0.2508
-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 )

0.2466
-29.0000
7.0000
I = N i j w i j i j w i j ( X i - X ¯ ) ( X j - X ¯ ) i ( X i - X ¯ ) 2

0.2466
-30.0000
8.0000
TREND = i = 1 N ~ ( i - N ~ / 2 ) ( R R i - R R i ) i = 1 N ~ ( i - N ~ / 2 ) 2 ,

0.2424
-16.0000
8.0000
1 M N i = 0 N - 1 j = 0 M - 1 ( I i j - I ¯ ) 2 ,

0.2337
-36.0000
10.0000
= [ 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

0.2332
-32.0000
9.0000
K = ( N - 1 ) i = 1 g n i ( r ¯ i - r ¯ ) 2 i = 1 g j = 1 n i ( r i j - r ¯ ) 2 ,

0.2332
-34.0000
9.0000
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

0.2332
-38.0000
9.0000
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 * ) .

0.2332
-43.0000
9.0000
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 ) .

0.2264
-18.0000
12.0000
i = 1 n x i 2 i = 1 n y i 2 - ( i = 1 n x i y i ) 2 0.

0.2230
-6.0000
9.0000
T = i = 1 n ( X i - μ ) 2 n .

0.2230
-7.0000
9.0000
Z n = i = 1 n ( X i - μ ) σ n

0.2230
-8.0000
9.0000
T = i = 1 n ( X i - μ ) 2 n + 2 .

0.2230
-15.0000
8.0000
s p 2 = i = 1 k ( n i - 1 ) s i 2 i = 1 k n i

0.2230
-18.0000
8.0000
s p 2 = i = 1 k ( n i - 1 ) s i 2 i = 1 k ( n i - 1 )

0.2230
-28.0000
7.0000
( X i - μ ) 2 = ( X i - X ¯ ) 2 + ( X ¯ - μ ) 2 + 2 ( X i - X ¯ ) ( X ¯ - μ ) .

0.2184
-1.0000
10.0000
i = 1 n ( x i - x ¯ n ) 2

0.2184
-2.0000
10.0000
i = 1 n ( a i - b i ) 2 .

0.2184
-6.0000
9.0000
d j k = i = 1 N ( x i j - x i k ) 2

0.2184
-29.0000
10.0000
( a 1 - b 1 ) 2 + ( a 2 - b 2 ) 2 + + ( a n - b n ) 2 = i = 1 n ( a i - b i ) 2 .

0.2184
-31.0000
8.0000
σ ^ 2 = 1 n i = 1 n ( μ - δ i ) 2 - 1 n 2 i = 1 n j = 1 n ( μ - δ i ) ( μ - δ j ) .

0.2018
-6.0000
9.0000
i j ( Y i j - Y ¯ i ) 2 / ( N - K ) ,

0.2018
-12.0000
8.0000
s 2 = i = 0 p j = 1 N i ( X i j - X i ¯ ) n

0.2018
-14.0000
9.0000
σ 2 = i = 1 N w i ( x i - x ¯ * ) 2 i = 1 N w i

0.1994
-19.0000
7.0000
r ( Y , Y ^ ) 2 = i ( Y ^ i - Y ¯ ) 2 i ( Y i - Y ¯ ) 2

0.1994
-19.0000
5.0000
η 2 = x n x ( y ¯ x - y ¯ ) 2 x , i ( y x i - y ¯ ) 2

0.1994
-21.0000
7.0000
S 3 = N - 1 i ( x i - x ¯ ) 4 ( N - 1 i ( x i - x ¯ ) 2 ) 2

0.1994
-23.0000
7.0000
i ( Y i - Y ¯ ) 2 = i ( Y i - Y ^ i ) 2 + i ( Y ^ i - Y ¯ ) 2 ,

0.1994
-35.0000
7.0000
1 = i ( Y i - Y ^ i ) 2 i ( Y i - Y ¯ ) 2 + i ( Y ^ i - Y ¯ ) 2 i ( Y i - Y ¯ ) 2 .

0.1942
-21.0000
9.0000
μ sig = i = 1 n ( X i - f i ) n μ bkg = i = 1 n ( X i - f i ) n

0.1942
-23.0000
9.0000
i = 1 n ( y i - y ^ i ) 2 = i = 1 n ( y i - j = 1 K β ^ j X i j ) 2 .

0.1942
-26.0000
7.0000
( N - 2 K ) ( N - 1 ) 1 2 ( N - 2 n ) [ n K ( N - K ) ( N - n ) ] 1 2 ( N - 2 )

0.1770
-12.0000
9.0000
s ¯ i = j = 1 n ( x i j - x ¯ i ) 2 n - 1

0.1770
-13.0000
7.0000
( y i - y ¯ ) = ( y i - y ^ i ) + ( y ^ i - y ¯ ) .

0.1758
-13.0000
6.0000
( X i - μ ) 2 = ( X i - X ¯ + X ¯ - μ ) 2

0.1616
-9.0000
7.0000
i = 1 n f ( x i * ) ( x i - x i - 1 )

0.1575
-12.0000
6.0000
Γ = ( r j - r i ) ( s j - s i ) ( r j - r i ) 2

0.1452
-12.0000
7.0000
i = 1 n x i ( 1 - k i ) ( 1 - k j ) - 1 = 0

0.1285
-12.0000
4.0000
( t - p ) ( t - q ) ( t - r ) ( t - s ) .