Returned 99 matches (100 formulae, 64 docs)
    Lookup 696.779 ms, Re-ranking 9956.327 ms
    Found 813116 tuple postings, 162979 formulae, 20880 documents
[ formulas ] [ documents ] [ documents-by-formula ]

k = 1 n ( x k - x ¯ ) ( y k - y ¯ ) k = 1 n ( x k - x ¯ ) 2 k = 1 n ( y k - y ¯ ) 2
Doc 1
0.8093, 0.8093
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dimensionless_quantity.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 ,
Doc 2
0.5449, 0.5449
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Correlation_and_dependence.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 3
0.4882, 0.4882
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Fisher_transformation.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 4
0.4390, 0.4390
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Assortativity.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
Doc 5
0.4198, 0.7847
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html
n ( X ¯ - μ 0 ) i = 1 n ( X i - X ¯ ) 2 / ( n - 1 )
Doc 6
0.4017, 1.1230
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html
b ^ = i = 1 n ( x i - x ¯ ) ( y i - y ¯ ) i = 1 n ( x i - x ¯ ) 2 ,
Doc 7
0.3671, 0.7275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.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 8
0.3546, 0.3546
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Collaborative_filtering.html
i = 1 n ( X i - X ¯ ) ( X i - X ¯ ) T W p ( Σ , n - 1 ) .
Doc 9
0.3257, 2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
i = 1 n ( x i - x ¯ ) ( θ - x ¯ ) = 0
Doc 10
0.3239, 0.3239
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sufficient_statistic.html
S n = 1 n i = 1 n ( X i - X ¯ ) ( X i - X ¯ ) T
Doc 9
0.3257, 2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
𝐐 𝐧 = 1 n i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T .
Doc 9
0.3257, 2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
𝐖 = 1 n - 1 i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ )
Doc 11
0.3135, 0.5630
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hotelling's_T-squared_distribution.html
i = 1 n ( X i - X ¯ ) 2 σ 2
Doc 6
0.4017, 1.1230
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html
𝐐 = 1 n - 1 i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T ,
Doc 9
0.3257, 2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
S = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T 𝐑 p × p .
Doc 9
0.3257, 2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
𝐐 = 1 N - 1 i = 1 N ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) T ,
Doc 12
0.3015, 0.8530
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html
s y m b o l Σ ^ = 1 n i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) T
Doc 13
0.2950, 0.7884
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Multivariate_normal_distribution.html
i = 1 n ( X i - X ¯ ) 2 = X 1 - X ¯ X n - X ¯ 2 .
Doc 6
0.4017, 1.1230
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).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 )
Doc 14
0.2884, 0.4507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kurtosis.html
t score = ( β ^ - β 0 ) n - 2 SSR / i = 1 n ( x i - x ¯ ) 2 .
Doc 15
0.2850, 0.5243
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html
r = 1 n - 1 i = 1 n ( X i - X ¯ ) ( Y i - Y ¯ ) s X s Y
Doc 16
0.2833, 0.2833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Pivotal_quantity.html
ρ i j ( a i j - a ¯ ) ( a j i - a ¯ ) i j ( a i j - a ¯ ) 2
Doc 17
0.2827, 0.2827
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Reciprocity_(network_science).html
s y m b o l Σ ^ = 1 n - 1 i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) T .
Doc 13
0.2950, 0.7884
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Multivariate_normal_distribution.html
𝐂 = i = 1 n ( 𝐱 𝐢 - 𝐱 ¯ ) ( 𝐱 𝐢 - 𝐱 ¯ ) T
Doc 18
0.2817, 0.5634
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Conjugate_prior.html
Doc 18
0.2817, 0.5634
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Conjugate_prior.html
i = 1 n ( y i - y ¯ ) ( x i - x ¯ ) - β ^ i = 1 n ( x i - x ¯ ) 2 = 0
Doc 19
0.2793, 0.5416
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Simple_linear_regression.html
q x y = ( x - x ¯ ) ( y - y ¯ ) I ( x , y ) I ( x , y )
Doc 20
0.2765, 0.2765
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Gravitational_lensing_formalism.html
σ X 2 = i = 1 n ( X i - X ¯ ) 2 n .
Doc 21
0.2751, 0.2751
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Kuder–Richardson_Formula_20.html
β 1 ^ = ( x i - x ¯ ) ( y i - y ¯ ) ( x i - x ¯ ) 2 and β 0 ^ = y ¯ - β 1 ^ x ¯
Doc 22
0.2718, 0.2718
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Regression_analysis.html
C n = i = 1 n ( x i - x ¯ n ) ( y i - y ¯ n )
Doc 23
0.2689, 0.8776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html
σ 2 = i = 1 n ( x i - x ¯ ) 2 / ( n - 1 )
Doc 24
0.2662, 0.3567
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html
i = 1 n ( x i - μ ) ( x i - μ ) T = i = 1 n ( x i - x ¯ ) ( x i - x ¯ ) T = S
Doc 9
0.3257, 2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.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 )
Doc 19
0.2793, 0.5416
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Simple_linear_regression.html
( x i - x ¯ ) T Σ - 1 ( x i - x ¯ )
Doc 9
0.3257, 2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
Σ b = 1 C i = 1 C ( μ i - μ ) ( μ i - μ ) T
Doc 25
0.2585, 0.2585
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Linear_discriminant_analysis.html
s = i = 1 n ( x i - x ¯ ) 2 n - 1
Doc 26
0.2543, 0.4328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html
i = 1 n ( X i - X ¯ ) 2
Doc 27
0.2523, 0.4184
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Bias_of_an_estimator.html
i = 1 n ( y i - y ¯ ) 2
Doc 28
0.2523, 0.2523
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Partition_of_sums_of_squares.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 11
0.3135, 0.5630
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hotelling's_T-squared_distribution.html
i = 1 n ( a i - b i ) 2 .
Doc 29
0.2448, 0.2448
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Absolute_value.html
S E β ^ = 1 n - 2 i = 1 n ( y i - y ^ i ) 2 i = 1 n ( x i - x ¯ ) 2
Doc 15
0.2850, 0.5243
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html
variance = s 2 = i = 1 n ( x i - x ¯ ) 2 n - 1
Doc 23
0.2689, 0.8776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html
q j k = 1 N i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k )
Doc 12
0.3015, 0.8530
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html
q j k = 1 N - 1 i = 1 N ( X i j - X ¯ j ) ( X i k - X ¯ k )
Doc 30
0.2270, 0.2270
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Covariance.html
q j k = 1 N - 1 i = 1 N ( x i j - x ¯ j ) ( x i k - x ¯ k ) ,
Doc 12
0.3015, 0.8530
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html
𝐱 ¯ = n - 1 i = 1 n 𝐱 i , 𝐒 = n - 1 i = 1 n ( 𝐱 i - 𝐱 ¯ ) ( 𝐱 i - 𝐱 ¯ ) .
Doc 13
0.2950, 0.7884
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Multivariate_normal_distribution.html
i j ( Y i j - Y ¯ i ) 2 / ( N - K ) ,
Doc 31
0.2081, 0.2081
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/F-test.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 32
0.2058, 0.2058
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Regression_toward_the_mean.html
d j k = i = 1 N ( x i j - x i k ) 2
Doc 33
0.2044, 0.2044
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Qualitative_variation.html
s M = i = 1 m x i ; s Σ = i = 1 m ( x i - x ¯ ) 2
Doc 34
0.2043, 0.2043
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Well-behaved_statistic.html
T = i = 1 n ( X i - μ ) 2 n .
Doc 35
0.2008, 0.3948
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cramér–Rao_bound.html
1 M N i = 0 N - 1 j = 0 M - 1 ( I i j - I ¯ ) 2 ,
Doc 36
0.1994, 0.1994
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Contrast_(vision).html
Z n = i = 1 n ( X i - μ ) σ n
Doc 37
0.1992, 0.1992
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Probability_theory.html
i = 1 n ( x i - x ¯ n ) 2
Doc 23
0.2689, 0.8776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html
T = i = 1 n ( X i - μ ) 2 n + 2 .
Doc 35
0.2008, 0.3948
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cramér–Rao_bound.html
β ^ = 1 T t = 1 T ( x t - x ¯ ) ( y t - y ¯ ) 1 T t = 1 T ( x t - x ¯ ) 2 ,
Doc 38
0.1875, 0.1875
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Errors-in-variables_models.html
σ 2 = i = 1 N w i ( x i - x ¯ * ) 2 i = 1 N w i
Doc 39
0.1872, 0.2834
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Mean_square_weighted_deviation.html
σ y 2 = 1 n i = 1 n ( y i - y ¯ ) 2 = ( 1 n i = 1 n y i 2 ) - y ¯ 2
Doc 40
0.1786, 0.1786
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Variance.html
s ¯ i = j = 1 n ( x i j - x ¯ i ) 2 n - 1
Doc 26
0.2543, 0.4328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html
s 2 = i = 1 n ( x i - K ) 2 - ( i = 1 n ( x i - K ) ) 2 / n n - 1 .
Doc 23
0.2689, 0.8776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.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 41
0.1710, 0.1710
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Experimental_uncertainty_analysis.html
1 n i = 1 n ( X i - X ¯ ) 2 < 1 n i = 1 n ( X i - μ ) 2 ,
Doc 27
0.2523, 0.4184
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Bias_of_an_estimator.html
Γ = ( r j - r i ) ( s j - s i ) ( r j - r i ) 2
Doc 42
0.1635, 0.1635
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rank_correlation.html
i = 1 n ( x i - μ ) 2 = i = 1 n ( x i - x ¯ ) 2 + n ( x ¯ - μ ) 2
Doc 43
0.1628, 0.1628
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Normal_distribution.html
s 2 = i = 0 p j = 1 N i ( X i j - X i ¯ ) n
Doc 44
0.1627, 0.1627
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Dunnett's_test.html
= ( 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 )
Doc 14
0.2884, 0.4507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kurtosis.html
s p 2 = i = 1 k ( n i - 1 ) s i 2 i = 1 k n i
Doc 45
0.1611, 0.3125
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Pooled_variance.html
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
Doc 46
0.1609, 0.1609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Tukey's_test_of_additivity.html
( a 1 - b 1 ) 2 + ( a 2 - b 2 ) 2 + + ( a n - b n ) 2 = i = 1 n ( a i - b i ) 2 .
Doc 47
0.1529, 0.1529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Pythagorean_theorem.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
Doc 48
0.1514, 0.1514
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Fixed_effects_model.html
s p 2 = i = 1 k ( n i - 1 ) s i 2 i = 1 k ( n i - 1 )
Doc 45
0.1611, 0.3125
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Pooled_variance.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 )
Doc 49
0.1440, 0.2815
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Omnibus_test.html
( y i - y ¯ ) = ( y i - y ^ i ) + ( y ^ i - y ¯ ) .
Doc 7
0.3671, 0.7275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html
r ( Y , Y ^ ) 2 = i ( Y ^ i - Y ¯ ) 2 i ( Y i - Y ¯ ) 2
Doc 5
0.4198, 0.7847
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html
i = 1 n f ( x i * ) ( x i - x i - 1 )
Doc 50
0.1394, 0.1394
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Antiderivative.html
i = 1 n x i 2 i = 1 n y i 2 - ( i = 1 n x i y i ) 2 0.
Doc 51
0.1386, 0.1386
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Cauchy–Schwarz_inequality.html
( X i - μ ) 2 = ( X i - X ¯ + X ¯ - μ ) 2
Doc 52
0.1382, 0.2585
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cochran's_theorem.html
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 49
0.1440, 0.2815
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Omnibus_test.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 53
0.1364, 0.1364
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Kruskal–Wallis_one-way_analysis_of_variance.html
i = 1 n ( y i - y ¯ ) 2 = i = 1 n ( y i - y ^ i ) 2 + i = 1 n ( y ^ i - y ¯ ) 2 .
Doc 7
0.3671, 0.7275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html
μ sig = i = 1 n ( X i - f i ) n μ bkg = i = 1 n ( X i - f i ) n
Doc 54
0.1316, 0.1316
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Signal-to-noise_ratio_(imaging).html
( N - 2 K ) ( N - 1 ) 1 2 ( N - 2 n ) [ n K ( N - K ) ( N - n ) ] 1 2 ( N - 2 )
Doc 55
0.1310, 0.1310
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hypergeometric_distribution.html
I = N i j w i j i j w i j ( X i - X ¯ ) ( X j - X ¯ ) i ( X i - X ¯ ) 2
Doc 56
0.1244, 0.2480
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 56
0.1244, 0.2480
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Moran's_I.html
( t - p ) ( t - q ) ( t - r ) ( t - s ) .
Doc 57
0.1231, 0.1231
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Brahmagupta.html
TREND = i = 1 N ~ ( i - N ~ / 2 ) ( R R i - R R i ) i = 1 N ~ ( i - N ~ / 2 ) 2 ,
Doc 58
0.1222, 0.1222
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Recurrence_quantification_analysis.html
i = 1 n ( y i - y ^ i ) 2 = i = 1 n ( y i - j = 1 K β ^ j X i j ) 2 .
Doc 59
0.1218, 0.1218
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Gauss–Markov_theorem.html
( X i - μ ) 2 = ( X i - X ¯ ) 2 + ( X ¯ - μ ) 2 + 2 ( X i - X ¯ ) ( X ¯ - μ ) .
Doc 52
0.1382, 0.2585
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cochran's_theorem.html
SSE = i = 1 n ( X i - X ¯ ) 2 + i = 1 n ( Y i - Y ¯ ) 2 + i = 1 n ( Z i - Z ¯ ) 2
Doc 6
0.4017, 1.1230
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html
i ( Y i - Y ¯ ) 2 = i ( Y i - Y ^ i ) 2 + i ( Y ^ i - Y ¯ ) 2 ,
Doc 5
0.4198, 0.7847
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.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 ,
Doc 60
0.1143, 0.1143
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Jarque–Bera_test.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
Doc 61
0.1122, 0.1122
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Bessel's_correction.html
i = 1 n x i ( 1 - k i ) ( 1 - k j ) - 1 = 0
Doc 62
0.1113, 0.1113
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Nakayama_lemma.html
η 2 = x n x ( y ¯ x - y ¯ ) 2 x , i ( y x i - y ¯ ) 2
Doc 63
0.1071, 0.1071
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Correlation_ratio.html
1 = i ( Y i - Y ^ i ) 2 i ( Y i - Y ¯ ) 2 + i ( Y ^ i - Y ¯ ) 2 i ( Y i - Y ¯ ) 2 .
Doc 5
0.4198, 0.7847
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html
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 ) .
Doc 64
0.0969, 0.0969
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Maximum_likelihood.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
Doc 39
0.1872, 0.2834
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Mean_square_weighted_deviation.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 ) .
Doc 12
0.3015, 0.8530
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.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 * ) .
Doc 24
0.2662, 0.3567
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html
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 ) .
Doc 7
0.3671, 0.7275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html