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relationship between the response (DV) and covariate (CV): y i j = μ + τ i + B ( x i j − x ¯ ) + ϵ i j . {\displaystyle y_{ij}=\mu +\tau _{i}+\mathrm {B} (x_{ij}-{\overline...

from simple linear regression y i ^ = a ^ + b ^ x i {\displaystyle {\hat {y_{i}}}={\hat {a}}+{\hat {b}}x_{i}} y ¯ = a ^ + b ^ x ¯ {\displaystyle {\bar...

q ) ∞ ∏ 1 ≤ i ≤ n ( x i 2 , 1 / x i 2 ; q ) ∞ ( a x i , a / x i , b x i , b / x i , c x i , c / x i , d x i , d / x i ; q ) ∞ {\displaystyle \prod _{1\leq...

dimension). A common panel data regression model looks like y i t = a + b x i t + ε i t {\displaystyle y_{it}=a+bx_{it}+\varepsilon _{it}} , where y {\displaystyle...

that there is some (indexed) collection of balls { B ( x i , r i ) : i ∈ I } {\displaystyle \{B(x_{i},r_{i}):i\in I\}} covering S with ri > 0 for each...

residuals e ^ i = y i − ( a ^ + b ^ x i ) {\displaystyle {\widehat {e}}_{i}=y_{i}-({\widehat {a}}+{\widehat {b}}x_{i})} are constrained to lie within...

i   δ δ   j μ b ( x )   i   δ δ   ε c ( x ) ) × exp ⁡ ( − i   g ∫ d 4 x   f a b c ∂ μ i   δ δ   j ν a ( x ) i   δ δ   j μ b ( x )   i   δ δ   j c ν (...

{\displaystyle (i,j)} belongs to the matching M {\displaystyle M} and b = x i ⊕ x j {\displaystyle b=x_{i}\oplus x_{j}} . It has been used to find quantum communication...

( B , X [ i ] ) → Hom ⁡ ( B , Y [ i ] ) → Hom ⁡ ( B , Z [ i ] ) → Hom ⁡ ( B , X [ i + 1 ] ) → ⋯ {\displaystyle \cdots \to \operatorname {Hom} (B,X[i])\to...

i = b = f ( x 1 , … , x i − 1 , b , x i + 1 , … , x n ) . {\displaystyle f|_{x_{i}=b}=f(x_{1},\ldots ,x_{i-1},b,x_{i+1},\ldots ,x_{n}).} In general, the...

{\displaystyle K} by a finite set of open balls { B ( x i , r ) } i = 1 , . . . , N {\displaystyle \{B(x_{i},r)\}_{i=1,...,N}} of radius r = ϵ M {\displaystyle...

{B(x)}{B^{\prime }(y_{i})(x-y_{i})}},} with A ( x ) = ∏ i = 1 n ( x − x i ) and B ( x ) = ∏ i = 1 n ( x − y i ) . {\displaystyle A(x)=\prod _{i=1}^{n}(x-x_{i})\quad...

columns indexed by integers 0...n, and entries B x , i = # { c ∈ C ∣ d ( c , x ) = i } . {\displaystyle B_{x,i}=\#\left\lbrace c\in C\mid d(c,x)=i\right\rbrace...

_{i=0}^{n}k_{i}x^{i}\right)\sin(bx)\!} ( ∑ i = 0 n Q i x i ) cos ⁡ ( b x ) + ( ∑ i = 0 n R i x i ) sin ⁡ ( b x ) {\displaystyle \left(\sum...

0 ) = arg ⁡ min β ( X 0 ) ∑ i = 1 N K h λ ( X 0 , X i ) ( Y ( X i ) − b ( X i ) T β ( X 0 ) ) 2 b ( X ) = ( 1 , X 1 , X 2 , . . . X 1 2 , X 2 2 , . ...

Q test statistic is T = k ( k − 1 ) ∑ j = 1 k ( X ∙ j − N k ) 2 ∑ i = 1 b X i ∙ ( k − X i ∙ ) {\displaystyle T=k\left(k-1\right){\frac {\sum \limits...

i ) x = c 1 e a x ( cos ⁡ b x + i sin ⁡ b x ) + c 2 e a x ( cos ⁡ b x − i sin ⁡ b x ) = ( c 1 + c 2 ) e a x cos ⁡ b x + i ( c 1 − c 2 ) e a x sin ⁡ b...

( ∏ i ∈ B X i ) {\displaystyle \kappa (X_{1},\dots ,X_{n})=\sum _{\pi }(|\pi |-1)!(-1)^{|\pi |-1}\prod _{B\in \pi }E\left(\prod _{i\in B}X_{i}\right)}...

that certain letters will precede or succeed other letters: P ( X i = b ∣ X i − 1 = a ) {\displaystyle P(X_{i}=b\mid X_{i-1}=a)} , or P ( X i = c ∣ X...

the other N / 2 {\displaystyle N/2} sensors use m B ( x ) = I ( x − τ 2 ) {\displaystyle m_{B}(x)=I(x-\tau _{2})} . The processing center estimation rule...