updated index pages

The index pages were updated with the recently added proofs/definitions.

Author: JoramSoch

I/DbA.md

@@ -8,7 +8,7 @@ title: "Definition by Author"
 
 - [Sample covariance](/D/cov-samp)
 
-### JoramSoch (178 definitions)
+### JoramSoch (180 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
@@ -65,6 +65,7 @@ title: "Definition by Author"
 - [Expected value of a random vector](/D/mean-rvec)
 - [Explained sum of squares](/D/ess)
 - [Exponential distribution](/D/exp)
+- [F-contrast for contrast-based inference in multiple linear regression](/D/fcon)
 - [F-distribution](/D/f)
 - [Family evidence](/D/fe)
 - [Flat, hard and soft prior distribution](/D/prior-flat)
@@ -173,6 +174,7 @@ title: "Definition by Author"
 - [Statistical hypothesis](/D/hyp)
 - [Statistical hypothesis test](/D/test)
 - [Statistical independence](/D/ind)
+- [t-contrast for contrast-based inference in multiple linear regression](/D/tcon)
 - [t-distribution](/D/t)
 - [Test statistic](/D/tstat)
 - [Total sum of squares](/D/tss)

I/DbN.md

@@ -191,3 +191,5 @@ title: "Definition by Number"
 | D182 | anova2 | [Two-way analysis of variance](/D/anova2) | JoramSoch | 2022-11-06 |
 | D183 | trss | [Treatment sum of squares](/D/trss) | JoramSoch | 2022-12-14 |
 | D184 | iass | [Interaction sum of squares](/D/iass) | JoramSoch | 2022-12-14 |
+| D185 | tcon | [t-contrast for contrast-based inference in multiple linear regression](/D/tcon) | JoramSoch | 2022-12-16 |
+| D186 | fcon | [F-contrast for contrast-based inference in multiple linear regression](/D/fcon) | JoramSoch | 2022-12-16 |

I/DbT.md

@@ -80,6 +80,7 @@ title: "Definition by Topic"
 
 ### F
 
+- [F-contrast for contrast-based inference in multiple linear regression](/D/fcon)
 - [F-distribution](/D/f)
 - [Family evidence](/D/fe)
 - [Flat, hard and soft prior distribution](/D/prior-flat)
@@ -229,6 +230,7 @@ title: "Definition by Topic"
 
 ### T
 
+- [t-contrast for contrast-based inference in multiple linear regression](/D/tcon)
 - [t-distribution](/D/t)
 - [Test statistic](/D/tstat)
 - [Total sum of squares](/D/tss)

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (369 proofs)
+### JoramSoch (375 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -83,9 +83,11 @@ title: "Proof by Author"
 - [Differential entropy of the normal distribution](/P/norm-dent)
 - [Differential entropy of the normal-gamma distribution](/P/ng-dent)
 - [Distribution of parameter estimates for simple linear regression](/P/slr-olsdist)
+- [Distribution of residual sum of squares in multiple linear regression with weighted least squares](/P/mlr-rssdist)
 - [Distribution of the inverse general linear model](/P/iglm-dist)
 - [Distribution of the transformed general linear model](/P/tglm-dist)
 - [Distributional transformation using cumulative distribution function](/P/cdf-dt)
+- [Distributions of estimated parameters, fitted signal and residuals in multiple linear regression upon weighted least squares](/P/mlr-wlsdist)
 - [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
 - [Entropy of the Bernoulli distribution](/P/bern-ent)
 - [Entropy of the binomial distribution](/P/bin-ent)
@@ -112,12 +114,15 @@ title: "Proof by Author"
 - [F-test for interaction in two-way analysis of variance](/P/anova2-fia)
 - [F-test for main effect in one-way analysis of variance](/P/anova1-f)
 - [F-test for main effect in two-way analysis of variance](/P/anova2-fme)
+- [F-test for multiple linear regression using contrast-based inference](/P/mlr-f)
 - [First central moment is zero](/P/momcent-1st)
 - [First raw moment is mean](/P/momraw-1st)
 - [Full width at half maximum for the normal distribution](/P/norm-fwhm)
 - [Gamma distribution is a special case of Wishart distribution](/P/gam-wish)
 - [Gaussian integral](/P/norm-gi)
 - [Gibbs' inequality](/P/gibbs-ineq)
+- [Independence of estimated parameters and residuals in multiple linear regression](/P/mlr-ind)
+- [Independence of products of multivariate normal random vector](/P/mvn-indprod)
 - [Inflection points of the probability density function of the normal distribution](/P/norm-infl)
 - [Invariance of the covariance matrix under addition of constant vector](/P/covmat-inv)
 - [Invariance of the differential entropy under addition of a constant](/P/dent-inv)
@@ -353,6 +358,7 @@ title: "Proof by Author"
 - [Symmetry of the covariance](/P/cov-symm)
 - [Symmetry of the covariance matrix](/P/covmat-symm)
 - [t-distribution is a special case of multivariate t-distribution](/P/t-mvt)
+- [t-test for multiple linear regression using contrast-based inference](/P/mlr-t)
 - [The p-value follows a uniform distribution under the null hypothesis](/P/pval-h0)
 - [The regression line goes through the center of mass point](/P/slr-comp)
 - [The residuals and the covariate are uncorrelated in simple linear regression](/P/slr-rescorr)

I/PbN.md

@@ -394,3 +394,9 @@ title: "Proof by Number"
 | P386 | mult-mll | [Maximum log-likelihood for multinomial observations](/P/mult-mll) | JoramSoch | 2022-12-02 |
 | P387 | mult-lbf | [Log Bayes factor for multinomial observations](/P/mult-lbf) | JoramSoch | 2022-12-02 |
 | P388 | mult-pp | [Posterior probability of the alternative model for multinomial observations](/P/mult-pp) | JoramSoch | 2022-12-02 |
+| P389 | mlr-wlsdist | [Distributions of estimated parameters, fitted signal and residuals in multiple linear regression upon weighted least squares](/P/mlr-wlsdist) | JoramSoch | 2022-12-13 |
+| P390 | mlr-rssdist | [Distribution of residual sum of squares in multiple linear regression with weighted least squares](/P/mlr-rssdist) | JoramSoch | 2022-12-13 |
+| P391 | mlr-t | [t-test for multiple linear regression using contrast-based inference](/P/mlr-t) | JoramSoch | 2022-12-13 |
+| P392 | mlr-f | [F-test for multiple linear regression using contrast-based inference](/P/mlr-f) | JoramSoch | 2022-12-13 |
+| P393 | mlr-ind | [Independence of estimated parameters and residuals in multiple linear regression](/P/mlr-ind) | JoramSoch | 2022-12-13 |
+| P394 | mvn-indprod | [Independence of products of multivariate normal random vector](/P/mvn-indprod) | JoramSoch | 2022-12-13 |

I/PbT.md

@@ -91,9 +91,11 @@ title: "Proof by Topic"
 - [Differential entropy of the normal distribution](/P/norm-dent)
 - [Differential entropy of the normal-gamma distribution](/P/ng-dent)
 - [Distribution of parameter estimates for simple linear regression](/P/slr-olsdist)
+- [Distribution of residual sum of squares in multiple linear regression with weighted least squares](/P/mlr-rssdist)
 - [Distribution of the inverse general linear model](/P/iglm-dist)
 - [Distribution of the transformed general linear model](/P/tglm-dist)
 - [Distributional transformation using cumulative distribution function](/P/cdf-dt)
+- [Distributions of estimated parameters, fitted signal and residuals in multiple linear regression upon weighted least squares](/P/mlr-wlsdist)
 
 ### E
 
@@ -127,6 +129,7 @@ title: "Proof by Topic"
 - [F-test for interaction in two-way analysis of variance](/P/anova2-fia)
 - [F-test for main effect in one-way analysis of variance](/P/anova1-f)
 - [F-test for main effect in two-way analysis of variance](/P/anova2-fme)
+- [F-test for multiple linear regression using contrast-based inference](/P/mlr-f)
 - [First central moment is zero](/P/momcent-1st)
 - [First raw moment is mean](/P/momraw-1st)
 - [Full width at half maximum for the normal distribution](/P/norm-fwhm)
@@ -139,6 +142,8 @@ title: "Proof by Topic"
 
 ### I
 
+- [Independence of estimated parameters and residuals in multiple linear regression](/P/mlr-ind)
+- [Independence of products of multivariate normal random vector](/P/mvn-indprod)
 - [Inflection points of the probability density function of the normal distribution](/P/norm-infl)
 - [Invariance of the covariance matrix under addition of constant vector](/P/covmat-inv)
 - [Invariance of the differential entropy under addition of a constant](/P/dent-inv)
@@ -419,6 +424,7 @@ title: "Proof by Topic"
 ### T
 
 - [t-distribution is a special case of multivariate t-distribution](/P/t-mvt)
+- [t-test for multiple linear regression using contrast-based inference](/P/mlr-t)
 - [The p-value follows a uniform distribution under the null hypothesis](/P/pval-h0)
 - [The regression line goes through the center of mass point](/P/slr-comp)
 - [The residuals and the covariate are uncorrelated in simple linear regression](/P/slr-rescorr)

P/mvn-indprod.md

@@ -49,7 +49,7 @@ $$
 Then, due to the [linear transformation theorem](/P/mvn-ltt), we have
 
 $$ \label{eq:CX}
-CZ = \left[ \begin{array}{c} AX \\ BX \end{array} \right] \sim \mathcal{N}\left( \left[ \begin{array}{c} A\mu \\ B\mu \end{array} \right], C \Sigma C^\mathrm{T} \right)
+CX = \left[ \begin{array}{c} AX \\ BX \end{array} \right] \sim \mathcal{N}\left( \left[ \begin{array}{c} A\mu \\ B\mu \end{array} \right], C \Sigma C^\mathrm{T} \right)
 $$
 
 with the combined [covariance matrix](/D/covmat)