17 Questions
What is the purpose of providing a confidence interval in statistics?
To provide a likely range that contains the true parameter value
What does a lower variance of an estimator indicate?
More precision
Which characteristic makes an estimator unbiased?
Having low bias
What does Mean Squared Error (MSE) in statistics measure?
Combination of bias and variance
In hypothesis testing, what is the primary purpose of making inferences using sample data?
To draw conclusions about population parameters
What does a 95% confidence level imply in interval estimation?
In 95% of repeated samples, the interval will contain the true parameter
What is the main goal of Ridge regression?
To introduce a regularization term to the least squares estimation
In the context of Ridge regression, what does the penalty term in the minimization function depend on?
Size of the coefficients
Which method is known for providing different approaches to estimate population parameters from sample data?
Maximum Likelihood Estimation
What makes Maximum Likelihood Estimation widely used and powerful?
Its desirable properties and asymptotic properties
What role does the Likelihood function play in estimating population parameters?
It helps in minimizing the squared residuals with respect to the coefficients
What does Maximum Likelihood Estimation seek to maximize?
The likelihood function
In Maximum Likelihood Estimation, what does the likelihood function measure?
The probability of observing the given sample
What is the mathematical representation of the likelihood function?
$L(\theta)=f(x_1;\theta)\times f(x_2;\theta)\times ... \times f(x_n;\theta)$
What does Bayesian Estimation incorporate along with the likelihood function?
Posterior distribution
In Least Squares Estimation, what is commonly minimized?
Sum of squared residuals
What concept does Least Squares Estimation minimize?
$\sum_{i=1}^n (y_i - f(x_i;\theta))^2$
This quiz covers the mathematical concept of how the posterior distribution is proportional to the prior distribution multiplied by the likelihood function, along with an explanation of Ridge Regression in statistics. Ridge Regression is used to tackle multicollinearity by introducing a regularization term to the least squares estimation. The procedure involves minimizing the sum of squared residuals and a penalty term based on the size of coefficients.
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