Returned 99 matches (100 formulae, 63 docs)
    Lookup 34.881 ms, Re-ranking 0.150 ms
    Found 408439 tuple postings, 134996 formulae, 19866 documents
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Doc 1
1.0000
1.1558
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Correlation_and_dependence.html
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 ,
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 .

Doc 2
0.5894
0.9348
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html
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
1 = i ( Y i - Y ^ i ) 2 i ( Y i - Y ¯ ) 2 + i ( Y ^ i - Y ¯ ) 2 i ( Y i - Y ¯ ) 2 .
r = r x y = x i y i - n x ¯ y ¯ ( n - 1 ) s x s y
Doc 3
0.4394
0.4394
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dimensionless_quantity.html
k = 1 n ( x k - x ¯ ) ( y k - y ¯ ) k = 1 n ( x k - x ¯ ) 2 k = 1 n ( y k - y ¯ ) 2

Doc 4
0.3290
0.8765
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html
b ^ = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) i = 1 n ( x i - x ¯ ) 2 ,
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 ) .
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 ) = 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.

Doc 5
0.3194
0.3194
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Fisher_transformation.html
r = i = 1 N ( X i - X ¯ ) ( Y i - Y ¯ ) i = 1 N ( X i - X ¯ ) 2 i = 1 N ( Y i - Y ¯ ) 2

Doc 6
0.2754
0.2754
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Regression_toward_the_mean.html
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 ,

Doc 7
0.2507
0.2507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Regression_analysis.html
β 1 ^ = ( x i - x ¯ ) ( y i - y ¯ ) ( x i - x ¯ ) 2 and β 0 ^ = y ¯ - β 1 ^ x ¯

Doc 8
0.2426
0.5500
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kurtosis.html
= ( 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 )
= ( 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 )
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
Doc 9
0.2353
0.4171
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html
S E β ^ = 1 n - 2 i = 1 n ( y i - y ^ i ) 2 i = 1 n ( x i - x ¯ ) 2
t score = ( β ^ - β 0 ) n - 2 SSR / i = 1 n ( x i - x ¯ ) 2 .

Doc 10
0.2163
0.2163
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Cosine_similarity.html
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

Doc 11
0.2161
0.6972
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Simple_linear_regression.html
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 )
i = 1 n ( y i - y ¯ ) ( x i - x ¯ ) - β ^ i = 1 n ( x i - x ¯ ) 2 = 0
r x y = x y ¯ - x ¯ y ¯ ( x 2 ¯ - x ¯ 2 ) ( y 2 ¯ - y ¯ 2 )
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

Doc 12
0.2120
0.4180
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Omnibus_test.html
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 )
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 )

Doc 13
0.2079
0.6905
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html
variance = s 2 = i = 1 n ( x i - x ¯ ) 2 n - 1
s 2 = i = 1 n ( x i - K ) 2 - ( i = 1 n ( x i - K ) ) 2 / n n - 1 .
C n = i = 1 n ( x i - x ¯ n ) ( y i - y ¯ n )
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 .

Doc 14
0.2042
0.2042
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Collaborative_filtering.html
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

Doc 15
0.2033
0.2033
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Assortativity.html
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 .

Doc 16
0.2031
0.2031
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Skewness.html
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 ,

Doc 17
0.2005
0.6609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Gravitational_lensing_formalism.html
q x y = ( x - x ¯ ) ( y - y ¯ ) w ( x - x ¯ , y - y ¯ ) I ( x , y ) w ( x - x ¯ , y - y ¯ ) I ( x , y )
q x y = ( x - x ¯ ) ( y - y ¯ ) I ( x , y ) I ( x , y )
q x x = ( x - x ¯ ) 2 w ( x - x ¯ , y - y ¯ ) I ( x , y ) w ( x - x ¯ , y - y ¯ ) I ( x , y )
q y y = ( y - y ¯ ) 2 w ( x - x ¯ , y - y ¯ ) I ( x , y ) w ( x - x ¯ , y - y ¯ ) I ( x , y )

Doc 18
0.1995
0.3930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Jarque–Bera_test.html
C = μ ^ 4 σ ^ 4 = 1 n i = 1 n ( x i - x ¯ ) 4 ( 1 n i = 1 n ( x i - x ¯ ) 2 ) 2 ,
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 ,

Doc 19
0.1978
0.4701
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html
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 ) .
q j k = 1 N i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k )
q j k = 1 N - 1 i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k ) ,
Doc 20
0.1971
0.6315
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
i = 1 n ( x i - μ ) ( x i - μ ) T = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T = S
𝐐 = 1 n - 1 i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T ,
𝐐 𝐧 = 1 n i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T .
S = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T 𝐑 p × p .

Doc 21
0.1956
0.1956
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hotelling's_T-squared_distribution.html
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

Doc 22
0.1916
0.1916
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/D'Agostino's_K-squared_test.html
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 ,

Doc 23
0.1891
0.1891
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Experimental_uncertainty_analysis.html
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

Doc 24
0.1816
0.1816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Errors-in-variables_models.html
β ^ = 1 T t = 1 T ( x t - x ¯ ) ( y t - y ¯ ) 1 T t = 1 T ( x t - x ¯ ) 2 ,

Doc 25
0.1806
0.3202
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Mean_absolute_difference.html
R M D ( S ) = i = 1 n j = 1 n | y i - y j | ( n - 1 ) i = 1 n y i
M D ( S ) = i = 1 n j = 1 n | y i - y j | n ( n - 1 )

Doc 26
0.1802
0.4889
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Fixed_effects_model.html
= [ 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
= 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 ) ]
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 ) ]
Doc 27
0.1757
0.2998
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html
n ( X ¯ - μ 0 ) i = 1 n ( X i - X ¯ ) 2 / ( n - 1 )
SSE = i = 1 n ( X i - X ¯ ) 2 + i = 1 n ( Y i - Y ¯ ) 2 + i = 1 n ( Z i - Z ¯ ) 2

Doc 28
0.1681
0.3290
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Bessel's_correction.html
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
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 .

Doc 29
0.1653
0.2998
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Ratio_estimator.html
r = y ¯ x ¯ = i = 1 n y i = 1 n x
var ( r ) = N - n N 1 m x 2 i = 1 n ( y i - r x i ) n - 1

Doc 30
0.1634
0.6292
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Mean_square_weighted_deviation.html
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
= 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
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 .
σ 2 = i = 1 N w i ( x i - x ¯ * ) 2 i = 1 N w i

Doc 31
0.1600
0.1600
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Weibull_distribution.html
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

Doc 32
0.1580
0.1580
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Vector_space_model.html
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

Doc 33
0.1570
0.1570
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Signal-to-noise_ratio_(imaging).html
μ sig = i = 1 n ( X i - f i ) n μ bkg = i = 1 n ( X i - f i ) n

Doc 34
0.1563
0.1563
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Moran's_I.html
S 3 = N - 1 i ( x i - x ¯ ) 4 ( N - 1 i ( x i - x ¯ ) 2 ) 2

Doc 35
0.1541
0.1541
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Pivotal_quantity.html
r = 1 n - 1 i = 1 n ( X i - X ¯ ) ( Y i - Y ¯ ) s X s Y

Doc 36
0.1523
0.1523
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Standardized_mean_of_a_contrast_variable.html
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

Doc 37
0.1519
0.2946
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Rational_trigonometry.html
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 ,
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 .

Doc 38
0.1504
0.3009
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Barycentric_coordinate_system.html
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 ) ,

Doc 39
0.1477
0.1477
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Gyration_tensor.html
S x y = 1 2 N 2 i = 1 N j = 1 N ( x i - x j ) ( y i - y j )

Doc 40
0.1476
0.2744
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html
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 * ) .
x ¯ = i = 1 n ( x i σ i - 2 ) i = 1 n σ i - 2 ,

Doc 41
0.1471
0.1471
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Normal_distribution.html
i = 1 n ( x i - μ ) 2 = i = 1 n ( x i - x ¯ ) 2 + n ( x ¯ - μ ) 2

Doc 42
0.1444
0.1444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dissociation_constant.html
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

Doc 43
0.1439
0.1439
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Fraction_of_variance_unexplained.html
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 .

Doc 44
0.1429
0.1429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Correlation_ratio.html
η 2 = x n x ( y ¯ x - y ¯ ) 2 x , i ( y x i - y ¯ ) 2

Doc 45
0.1404
0.1404
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Kernel_regression.html
m ^ h ( x ) = i = 1 n K h ( x - x i ) y i i = 1 n K h ( x - x i )

Doc 46
0.1388
0.1388
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/V-statistic.html
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 ,

Doc 47
0.1370
0.1370
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html
s = i = 1 n ( x i - x ¯ ) 2 n - 1

Doc 48
0.1346
0.1346
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Pooled_variance.html
s p 2 = i = 1 k ( n i - 1 ) s i 2 i = 1 k ( n i - 1 )

Doc 49
0.1331
0.1331
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Ky_Fan_inequality.html
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 )

Doc 50
0.1327
0.1327
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Image_moment.html
μ p q = x y ( x - x ¯ ) p ( y - y ¯ ) q f ( x , y )

Doc 51
0.1323
0.1323
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Concordance_correlation_coefficient.html
s x y = 1 N n = 1 N ( x n - x ¯ ) ( y n - y ¯ ) .

Doc 52
0.1313
0.1313
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Ordinary_least_squares.html
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

Doc 53
0.1309
0.1309
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Kruskal–Wallis_one-way_analysis_of_variance.html
K = ( N - 1 ) i = 1 g n i ( r ¯ i - r ¯ ) 2 i = 1 g j = 1 n i ( r i j - r ¯ ) 2 ,

Doc 54
0.1301
0.1301
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sufficient_statistic.html
i = 1 n ( x i - x ¯ ) ( θ - x ¯ ) = 0

Doc 55
0.1300
0.1300
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Cauchy–Schwarz_inequality.html
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 .

Doc 56
0.1299
0.1299
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Standard_deviation.html
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 .

Doc 57
0.1278
0.1278
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rank_correlation.html
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

Doc 58
0.1272
0.1272
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Elliptic_rational_functions.html
R n ( ξ , x ) = r 0 x i = 1 n - 1 ( x - x i ) i = 1 n - 1 ( x - x p i )

Doc 59
0.1268
0.1268
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Well-behaved_statistic.html
s M = i = 1 m x i ; s Σ = i = 1 m ( x i - x ¯ ) 2

Doc 60
0.1262
0.1262
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Intraclass_correlation.html
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 }

Doc 61
0.1253
0.1253
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Variance.html
σ y 2 = 1 n i = 1 n ( y i - y ¯ ) 2 = ( 1 n i = 1 n y i 2 ) - y ¯ 2

Doc 62
0.1246
0.1246
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Minimum_mean_square_error.html
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 .

Doc 63
0.1236
0.1236
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Rayleigh_quotient.html
R ( M , x ) = x * M x x * x = i = 1 n λ i y i 2 i = 1 n y i 2