query: How does $\vec{\beta}=(H^TH)^{-1}H^T\vec{y}$ equivalent to least squares criteria for evaluating splines?
positive_passages.docid: 29429
positive_passages.text: What algorithm is used in linear regression?
negative_passages.docid: 73073
negative_passages.text: Differentiating $y=x^{2}$
negative_passages.docid: 12703
negative_passages.text: Extracting polynomials from a cubic spline function
negative_passages.docid: 49984
negative_passages.text: Valid justification for algebraic manipulation of $\mathrm{d}y/\mathrm{d}x$?
negative_passages.docid: 146656
negative_passages.text: Multivariate Application of Slutsky's lemma
negative_passages.docid: 81748
negative_passages.text: Arc length parameterization lying on a sphere
negative_passages.docid: 112179
negative_passages.text: Why don't the results of testing $H_0 : \beta = 0$ and $H_0 : {\rm cor}(X,Y)=0$ agree?
negative_passages.docid: 68301
negative_passages.text: Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points (quantiles)
negative_passages.docid: 3998
negative_passages.text: Magnitude of standardized coefficients (beta) in multiple linear regression
negative_passages.docid: 152781
negative_passages.text: Chain rule for multivariable functions confusion
negative_passages.docid: 76853
negative_passages.text: Interpretation of $\mathbf{y}^T(\mathbf{I}-\mathbf{H})\mathbf{y}$ in OLS
negative_passages.docid: 158185
negative_passages.text: Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions
negative_passages.docid: 105248
negative_passages.text: Why is the gradient of implicit surface the normal vector (i.e. parallel to the normal line)?
negative_passages.docid: 42427
negative_passages.text: Understanding linear algebra in Ordinary Least Squares derivation
negative_passages.docid: 7241
negative_passages.text: Areas versus volumes of revolution: why does the area require approximation by a cone?
negative_passages.docid: 90370
negative_passages.text: How to derive the ridge regression solution?
negative_passages.docid: 59989
negative_passages.text: Comparing smoothing splines vs loess for smoothing?