Recent questions tagged linear-regression

Which of the following statements are true for a design matrix $X \in \mathbb{R}^{n \times d}$ with $d n$? (The rows are $n$ sample points and the columns represent $d$ ...

   

A data scientist uses LASSO regression on a training dataset and obtains a set of weights. LASSO is known for introducing bias due to its regularization penalty but is al...

You have used Ridge regression (12 penalty) on a dataset and obtained a set of weights 𝑤̂. Compared to the weights obtained from unregularized linear regression (Ordinary...

Consider linear regression and logistic regression. They both use linear functions.They both can be used to solve regression prob-They both use the logistic activation fu...

Consider a simple classification task with features $x_i \in \mathbb{R}^d$ and $k$ classes. Suppose we train a linear classifier to minimize the regularized least squared...

Consider just the general shape of the following plots.For each of the following possible interpretations of the quantities being plotted on the $X$ and $Y$ axes, indicat...

A linear model is defined as a model where our prediction $\hat{y}$ is given by the equation below, where $d$ is the number of parameters in our model:$$\hat{y}=f_\theta(...

$\text { Which model would be the most appropriate linear model for the following dataset ? }$ $ \ y=\theta_1 x+\theta_2 $$y=\sum_{k=1}^d \theta_k x^k $$\sqrt{ } y=\theta...

Suppose we have a data set of 100 points whose first few rows are shown below, and that we'd like to predict $\vec{y}$ from $\vec{v}$ and $\vec{w}$. Suppose we create a d...

Suppose we have a data set of 100 points whose first few rows are shown below, and that we'd like to predict $\vec{y}$ from $\vec{v}$ and $\vec{w}$. Suppose we create a d...

Suppose we have a data set of 100 points whose first few rows are shown below, and that we'd like to predict $\vec{y}$ from $\vec{v}$ and $\vec{w}$. Suppose we create a d...

Alice has collected a dataset of dependent and independent variables $\left\{\left(x^{(1)}, y^{(1)}\right), \ldots,\left(x^{(n)}, y^{(n)}\right)\right\}$; she does linear...

Let $(x_i, y_i)$ be a data point, where $x_i \in \mathbb{R}^d$ is a feature vector and $y_i \in \mathbb{R}$ is the correspondingoutput. There are a total of $m$ data poin...

For the remainder of this question, we will use the multiple linear regression model, which is of the form$$\hat{y}=x \cdot \theta=\sum_{j=0}^p \theta_j x_j$$We assume th...

Given data $\mathcal{D}=\left\{\left(\mathbf{x}^{(1)}, y^{(1)}, \ldots,\left(\mathbf{x}^{(N)}, y^{(N)}\right)\right\}\right.$, we obtain $\hat{\mathbf{w}}$, the parameter...

Suppose the scores of the midterm, homework, and final of 4 students are given by MidtermHomeworkFinal808596726874949790697078You'd like to use linear regression to predi...

The closed form solution for linear regression is $\theta=\left(\mathbf{X}^T \mathbf{X}\right)^{-1} \mathbf{X}^T \mathbf{y}$. Suppose you have $N=35$ training examples an...