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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?

Combination of bias and variance Signup and view all the answers

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

To draw conclusions about population parameters Signup and view all the answers

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

In 95% of repeated samples, the interval will contain the true parameter Signup and view all the answers

What is the main goal of Ridge regression?

To introduce a regularization term to the least squares estimation Signup and view all the answers

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

Size of the coefficients Signup and view all the answers

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

Maximum Likelihood Estimation Signup and view all the answers

What makes Maximum Likelihood Estimation widely used and powerful?

Its desirable properties and asymptotic properties Signup and view all the answers

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

It helps in minimizing the squared residuals with respect to the coefficients Signup and view all the answers

What does Maximum Likelihood Estimation seek to maximize?

The likelihood function Signup and view all the answers

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

The probability of observing the given sample Signup and view all the answers

What is the mathematical representation of the likelihood function?

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

What does Bayesian Estimation incorporate along with the likelihood function?

Posterior distribution Signup and view all the answers

In Least Squares Estimation, what is commonly minimized?

Sum of squared residuals Signup and view all the answers

What concept does Least Squares Estimation minimize?

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