query: Proof for "The sum of the observed values $Y_i$ equals the sum of the estimated / fitted values $\hat Y_i$"
positive_passages.docid: 20216
positive_passages.text: Why do residuals in linear regression always sum to zero when an intercept is included?
negative_passages.docid: 8007
negative_passages.text: Proof of Young's inequality
negative_passages.docid: 139692
negative_passages.text: Proof of inequality using AM-GM inequality
negative_passages.docid: 71203
negative_passages.text: Proving that two systems of linear equations are equivalent if they have the same solutions
negative_passages.docid: 62513
negative_passages.text: Proving that the estimate of a mean is a least squares estimator?
negative_passages.docid: 67454
negative_passages.text: Show that $\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^n (x_i - \bar{x})(y_i)$.
negative_passages.docid: 51967
negative_passages.text: Prove that if the sum of each row of $A$ equals $s$, then $s$ is an eigenvalue of $A$.
negative_passages.docid: 90215
negative_passages.text: Proof/Derivation of Residual Sum of Squares (Based on Introduction to Statistical Learning)
negative_passages.docid: 69474
negative_passages.text: Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow  P_{j}P_{i}=0$
negative_passages.docid: 106140
negative_passages.text: The sum of two symmetric random variables is symmetric
negative_passages.docid: 65783
negative_passages.text: Proving: "The trace of an idempotent matrix equals the rank of the matrix"
negative_passages.docid: 73367
negative_passages.text: On $E[E[Y|X]|X]= E[Y|X]$
negative_passages.docid: 2898
negative_passages.text: What's the MSE of $\hat{Y}$ in ordinary least squares using bias-variance decomposition?
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 97733
negative_passages.text: Can it be determined that the sum of the diagonal entries, of matrix A, equals the sum of eigenvalues of A
negative_passages.docid: 88473
negative_passages.text: Proof that the trace of a matrix is the sum of its eigenvalues
negative_passages.docid: 124827
negative_passages.text: Show that $Y\sim N(a+A\mu,AVA^T)$