Mathematics and Ridge Regression
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Questions and Answers

What is the purpose of providing a confidence interval in statistics?

  • To determine the bias in an estimator
  • To provide a likely range that contains the true parameter value (correct)
  • To estimate a single value accurately
  • To calculate the variance of an estimator

What does a lower variance of an estimator indicate?

  • No impact on precision
  • Less precision
  • Higher bias
  • More precision (correct)

Which characteristic makes an estimator unbiased?

  • Having high mean squared error
  • Having no variance
  • Having low bias (correct)
  • Having the highest variability

What does Mean Squared Error (MSE) in statistics measure?

<p>Combination of bias and variance (D)</p> Signup and view all the answers

In hypothesis testing, what is the primary purpose of making inferences using sample data?

<p>To draw conclusions about population parameters (B)</p> Signup and view all the answers

What does a 95% confidence level imply in interval estimation?

<p>In 95% of repeated samples, the interval will contain the true parameter (C)</p> Signup and view all the answers

What is the main goal of Ridge regression?

<p>To introduce a regularization term to the least squares estimation (D)</p> Signup and view all the answers

In the context of Ridge regression, what does the penalty term in the minimization function depend on?

<p>Size of the coefficients (A)</p> Signup and view all the answers

Which method is known for providing different approaches to estimate population parameters from sample data?

<p>Maximum Likelihood Estimation (A)</p> Signup and view all the answers

What makes Maximum Likelihood Estimation widely used and powerful?

<p>Its desirable properties and asymptotic properties (B)</p> Signup and view all the answers

What role does the Likelihood function play in estimating population parameters?

<p>It helps in minimizing the squared residuals with respect to the coefficients (C)</p> Signup and view all the answers

What does Maximum Likelihood Estimation seek to maximize?

<p>The likelihood function (B)</p> Signup and view all the answers

In Maximum Likelihood Estimation, what does the likelihood function measure?

<p>The probability of observing the given sample (C)</p> Signup and view all the answers

What is the mathematical representation of the likelihood function?

<p>$L(\theta)=f(x_1;\theta)\times f(x_2;\theta)\times ... \times f(x_n;\theta)$ (A)</p> Signup and view all the answers

What does Bayesian Estimation incorporate along with the likelihood function?

<p>Posterior distribution (A)</p> Signup and view all the answers

In Least Squares Estimation, what is commonly minimized?

<p>Sum of squared residuals (C)</p> Signup and view all the answers

What concept does Least Squares Estimation minimize?

<p>$\sum_{i=1}^n (y_i - f(x_i;\theta))^2$ (D)</p> Signup and view all the answers

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