updated index pages

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

Author: JoramSoch

I/Definition_by_Author.md

@@ -4,7 +4,7 @@ title: "Definition by Author"
 ---
 
 
-### JoramSoch (157 definitions)
+### JoramSoch (159 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
@@ -129,6 +129,7 @@ title: "Definition by Author"
 - [Random vector](/D/rvec)
 - [Raw moment](/D/mom-raw)
 - [Reference prior distribution](/D/prior-ref)
+- [Regression line](/D/regline)
 - [Residual sum of squares](/D/rss)
 - [Residual variance](/D/resvar)
 - [Residual-forming matrix](/D/rfmat)
@@ -140,6 +141,7 @@ title: "Definition by Author"
 - [Signal-to-noise ratio](/D/snr)
 - [Significance level](/D/alpha)
 - [Simple and composite hypothesis](/D/hyp-simp)
+- [Simple linear regression](/D/slr)
 - [Size of a statistical test](/D/size)
 - [Standard deviation](/D/std)
 - [Standard gamma distribution](/D/sgam)

I/Definition_by_Number.md

@@ -169,3 +169,5 @@ title: "Definition by Number"
 | D160 | tglm | [Transformed general linear model](/D/tglm) | JoramSoch | 2021-10-21 |
 | D161 | iglm | [Inverse general linear model](/D/iglm) | JoramSoch | 2021-10-21 |
 | D162 | cfm | [Corresponding forward model](/D/cfm) | JoramSoch | 2021-10-21 |
+| D163 | slr | [Simple linear regression](/D/slr) | JoramSoch | 2021-10-27 |
+| D164 | regline | [Regression line](/D/regline) | JoramSoch | 2021-10-27 |

I/Definition_by_Topic.md

@@ -181,6 +181,7 @@ title: "Definition by Topic"
 - [Random vector](/D/rvec)
 - [Raw moment](/D/mom-raw)
 - [Reference prior distribution](/D/prior-ref)
+- [Regression line](/D/regline)
 - [Residual sum of squares](/D/rss)
 - [Residual variance](/D/resvar)
 - [Residual-forming matrix](/D/rfmat)
@@ -196,6 +197,7 @@ title: "Definition by Topic"
 - [Signal-to-noise ratio](/D/snr)
 - [Significance level](/D/alpha)
 - [Simple and composite hypothesis](/D/hyp-simp)
+- [Simple linear regression](/D/slr)
 - [Size of a statistical test](/D/size)
 - [Standard deviation](/D/std)
 - [Standard gamma distribution](/D/sgam)

I/Proof_by_Author.md

@@ -4,7 +4,7 @@ title: "Proof by Author"
 ---
 
 
-### JoramSoch (260 proofs)
+### JoramSoch (270 proofs)
 
 - [(Non-)Multiplicativity of the expected value](/P/mean-mult)
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
@@ -63,11 +63,13 @@ title: "Proof by Author"
 - [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)
+- [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)
 - [Equivalence of parameter estimates from the transformed general linear model](/P/tglm-para)
 - [Exceedance probabilities for the Dirichlet distribution](/P/dir-ep)
 - [Existence of a corresponding forward model](/P/cfm-exist)
 - [Expectation of a quadratic form](/P/mean-qf)
+- [Expectation of parameter estimates for simple linear regression](/P/slr-olsmean)
 - [Expectation of the cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbfmean)
 - [Expectation of the log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbfmean)
 - [Expected value of a non-negative random variable](/P/mean-nnrvar)
@@ -160,6 +162,7 @@ title: "Proof by Author"
 - [One-sample z-test for independent observations](/P/ugkv-ztest1)
 - [Ordinary least squares for multiple linear regression](/P/mlr-ols)
 - [Ordinary least squares for multiple linear regression](/P/mlr-ols2)
+- [Ordinary least squares for simple linear regression](/P/slr-ols)
 - [Ordinary least squares for the general linear model](/P/glm-ols)
 - [Paired t-test for dependent observations](/P/ug-ttestp)
 - [Paired z-test for dependent observations](/P/ugkv-ztestp)
@@ -236,6 +239,8 @@ title: "Proof by Author"
 - [Relation of mutual information to marginal and conditional entropy](/P/dmi-mce)
 - [Relation of mutual information to marginal and joint entropy](/P/dmi-mje)
 - [Relationship between R² and maximum log-likelihood](/P/rsq-mll)
+- [Relationship between coefficient of determination and correlation coefficient in simple linear regression](/P/slr-rsq)
+- [Relationship between correlation coefficient and slope estimate in simple linear regression](/P/slr-corr)
 - [Relationship between covariance and correlation](/P/cov-corr)
 - [Relationship between covariance matrix and correlation matrix](/P/covmat-corrmat)
 - [Relationship between gamma distribution and standard gamma distribution](/P/gam-sgam)
@@ -248,15 +253,20 @@ title: "Proof by Author"
 - [Relationship between normal distribution and standard normal distribution](/P/norm-snorm3)
 - [Relationship between normal distribution and t-distribution](/P/norm-t)
 - [Relationship between precision matrix and correlation matrix](/P/precmat-corrmat)
+- [Relationship between residual variance and sample variance in simple linear regression](/P/slr-resvar)
 - [Relationship between second raw moment, variance and mean](/P/momraw-2nd)
 - [Relationship between signal-to-noise ratio and R²](/P/snr-rsq)
 - [Scaling of the variance upon multiplication with a constant](/P/var-scal)
 - [Second central moment is variance](/P/momcent-2nd)
+- [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)
+- [The sum of residuals is zero in simple linear regression](/P/slr-ressum)
 - [Transformation matrices for ordinary least squares](/P/mlr-mat)
 - [Transposition of a matrix-normal random variable](/P/matn-trans)
 - [Two-sample t-test for independent observations](/P/ug-ttest2)
 - [Two-sample z-test for independent observations](/P/ugkv-ztest2)
 - [Variance of constant is zero](/P/var-const)
+- [Variance of parameter estimates for simple linear regression](/P/slr-olsvar)
 - [Variance of the Poisson distribution](/P/poiss-var)
 - [Variance of the beta distribution](/P/beta-var)
 - [Variance of the gamma distribution](/P/gam-var)

I/Proof_by_Number.md

@@ -276,3 +276,13 @@ title: "Proof by Number"
 | P268 | iglm-blue | [Best linear unbiased estimator for the inverse general linear model](/P/iglm-blue) | JoramSoch | 2021-10-21 |
 | P269 | cfm-para | [Parameters of the corresponding forward model](/P/cfm-para) | JoramSoch | 2021-10-21 |
 | P270 | cfm-exist | [Existence of a corresponding forward model](/P/cfm-exist) | JoramSoch | 2021-10-21 |
+| P271 | slr-ols | [Ordinary least squares for simple linear regression](/P/slr-ols) | JoramSoch | 2021-10-27 |
+| P272 | slr-olsmean | [Expectation of parameter estimates for simple linear regression](/P/slr-olsmean) | JoramSoch | 2021-10-27 |
+| P273 | slr-olsvar | [Variance of parameter estimates for simple linear regression](/P/slr-olsvar) | JoramSoch | 2021-10-27 |
+| P274 | slr-meancent | [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent) | JoramSoch | 2021-10-27 |
+| P275 | slr-comp | [The regression line goes through the center of mass point](/P/slr-comp) | JoramSoch | 2021-10-27 |
+| P276 | slr-ressum | [The sum of residuals is zero in simple linear regression](/P/slr-ressum) | JoramSoch | 2021-10-27 |
+| P277 | slr-rescorr | [The residuals and the covariate are uncorrelated in simple linear regression](/P/slr-rescorr) | JoramSoch | 2021-10-27 |
+| P278 | slr-resvar | [Relationship between residual variance and sample variance in simple linear regression](/P/slr-resvar) | JoramSoch | 2021-10-27 |
+| P279 | slr-corr | [Relationship between correlation coefficient and slope estimate in simple linear regression](/P/slr-corr) | JoramSoch | 2021-10-27 |
+| P280 | slr-rsq | [Relationship between coefficient of determination and correlation coefficient in simple linear regression](/P/slr-rsq) | JoramSoch | 2021-10-27 |

I/Proof_by_Topic.md

@@ -79,12 +79,14 @@ title: "Proof by Topic"
 
 ### E
 
+- [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
 - [Encompassing Prior Method for computing Bayes Factors](/P/bf-ep)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)
 - [Equivalence of parameter estimates from the transformed general linear model](/P/tglm-para)
 - [Exceedance probabilities for the Dirichlet distribution](/P/dir-ep)
 - [Existence of a corresponding forward model](/P/cfm-exist)
 - [Expectation of a quadratic form](/P/mean-qf)
+- [Expectation of parameter estimates for simple linear regression](/P/slr-olsmean)
 - [Expectation of the cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbfmean)
 - [Expectation of the log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbfmean)
 - [Expected value of a non-negative random variable](/P/mean-nnrvar)
@@ -207,6 +209,7 @@ title: "Proof by Topic"
 - [One-sample z-test for independent observations](/P/ugkv-ztest1)
 - [Ordinary least squares for multiple linear regression](/P/mlr-ols)
 - [Ordinary least squares for multiple linear regression](/P/mlr-ols2)
+- [Ordinary least squares for simple linear regression](/P/slr-ols)
 - [Ordinary least squares for the general linear model](/P/glm-ols)
 
 ### P
@@ -294,6 +297,8 @@ title: "Proof by Topic"
 - [Relation of mutual information to marginal and conditional entropy](/P/dmi-mce)
 - [Relation of mutual information to marginal and joint entropy](/P/dmi-mje)
 - [Relationship between R² and maximum log-likelihood](/P/rsq-mll)
+- [Relationship between coefficient of determination and correlation coefficient in simple linear regression](/P/slr-rsq)
+- [Relationship between correlation coefficient and slope estimate in simple linear regression](/P/slr-corr)
 - [Relationship between covariance and correlation](/P/cov-corr)
 - [Relationship between covariance matrix and correlation matrix](/P/covmat-corrmat)
 - [Relationship between gamma distribution and standard gamma distribution](/P/gam-sgam)
@@ -306,6 +311,7 @@ title: "Proof by Topic"
 - [Relationship between normal distribution and standard normal distribution](/P/norm-snorm3)
 - [Relationship between normal distribution and t-distribution](/P/norm-t)
 - [Relationship between precision matrix and correlation matrix](/P/precmat-corrmat)
+- [Relationship between residual variance and sample variance in simple linear regression](/P/slr-resvar)
 - [Relationship between second raw moment, variance and mean](/P/momraw-2nd)
 - [Relationship between signal-to-noise ratio and R²](/P/snr-rsq)
 
@@ -317,6 +323,9 @@ title: "Proof by Topic"
 
 ### T
 
+- [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)
+- [The sum of residuals is zero in simple linear regression](/P/slr-ressum)
 - [Transformation matrices for ordinary least squares](/P/mlr-mat)
 - [Transitivity of Bayes Factors](/P/bf-trans)
 - [Transposition of a matrix-normal random variable](/P/matn-trans)
@@ -326,6 +335,7 @@ title: "Proof by Topic"
 ### V
 
 - [Variance of constant is zero](/P/var-const)
+- [Variance of parameter estimates for simple linear regression](/P/slr-olsvar)
 - [Variance of the Poisson distribution](/P/poiss-var)
 - [Variance of the Wald distribution](/P/wald-var)
 - [Variance of the beta distribution](/P/beta-var)

I/Proofs_without_Source.md

@@ -21,6 +21,7 @@ title: "Proofs without Source"
 - [Derivation of the log model evidence](/P/lme-der)
 - [Derivation of the posterior model probability](/P/pmp-der)
 - [Differential entropy of the normal-gamma distribution](/P/ng-dent)
+- [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
 - [Expectation of the cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbfmean)
 - [Expectation of the log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbfmean)
 - [Exponential distribution is a special case of gamma distribution](/P/exp-gam)