Search Results

When you have $n$ points on a graph, there are many curves you can draw to pass through those $n$ points, provided no two points have a same $x$-coordinate and different $y$-coordinate. Since RSS depe …

Why does minimizing $$RSS(f) = \sum_{i=1}^N(y_i - f(x_i))^2$$ lead to infinitely many solutions? I saw it from the book The Elements of Statistical Learning,second edition (Chapter 2 section 2.7 under …

I was learning from Elements of statistics p.120 under section 4.4.1 Fitting Logistics Regression Models The log likelihood function was given as $l(\beta) = \sum_{i=1}^N {y_i\log p(x_i;\beta) + (1-y_i … When we find $\beta$ using linear regression, it will be a vector in $R^3$ or the vector will contain three elements i.e $\beta = \{ b_1,b_2,b_3 \}$ How did they get $\beta_{10}$ in $(1)$ and also I want …

Elements of statistics p.66 Please I know the least squares solution for $\hat\beta = (X^TX)^{-1}X^Ty$ but I don't know how they were able to get $X\hat\beta= X(X^TX)^{-1}X^Ty = UU^Ty$ These are the …

I was reading about variance of estimators and i saw Var(b̂) = σ2 / Inner product of (Z) where Z is the residual vector of Gram-Schmidt process. I do not understand how they were able to get the …

How do I differentiate $$ (y-X\beta)^T(y - X \beta) $$ with respect to $\beta$. The result I saw was $$X^T(y - X\beta)$$

Whiles reading An Introduction To Statistical Learning under linear regression (Chapter 3), I found: $$E(Y - \hat{Y})^2 = |f(X) - \hat{f}(X)|^2 + Var(ε)$$ where $E(Y - \hat{Y})^2$ represents the average …

I was reading from The Elements of Statistical Learning (Section 3.2) and they were able to find $Var(\hat\beta)$ Given $$\hat\beta = (X^TX)^{-1}X^Ty \qquad (3.6) $$ The answer they had was $Var(\hat\ …