What are the consequences of violating the homoscedasticity assumption in multiple linear regression?
- The R-squared value becomes negative
- The estimated regression coefficients are biased
- The regression line is not straight
- The standard errors are no longer valid
Violating the assumption of homoscedasticity (constant variance of the errors) can lead to inefficient and invalid standard errors, which can result in incorrect inferences about the regression coefficients. The regression coefficients themselves remain unbiased.
What can be the effect of overfitting in polynomial regression?
- The model will be easier to interpret
- The model will have high bias
- The model will perform poorly on new data
- The model will perform well on new data
Overfitting in polynomial regression means that the model fits the training data too closely, capturing not only the underlying pattern but also the noise. As a result, the model will perform well on the training data but poorly on new, unseen data. This is because the model has essentially 'memorized' the training data and fails to generalize well to new situations.
What happens to the width of the confidence interval when the sample variability increases?
- The interval becomes narrower
- The interval becomes skewed
- The interval becomes wider
- The interval does not change
The width of the confidence interval increases as the variability in the sample increases. Greater variability leads to a larger standard error, which in turn leads to wider confidence intervals.
When a servlet encounters an error during initialization, which method gets invoked next?
- destroy()
- doError()
- initError()
- service()
If a servlet encounters an error during initialization, the initError() method is invoked next to handle the initialization error.
If a client application needs to request a large amount of data without affecting the server's state, which method should it use and why?
- DELETE, because it is a safe method for retrieving data.
- GET, because it is idempotent and does not modify the server's state.
- POST, because it supports larger data payloads than GET.
- PUT, because it is specifically designed for requesting large data sets.
The GET method is idempotent and does not modify the server's state, making it suitable for requesting large amounts of data without side effects. POST, although supporting larger payloads, is not intended for safe, idempotent operations.
What is the significance of the Last-Modified header in HTTP servlet responses?
- It controls the cache behavior for the servlet response.
- It indicates the last modification time of the servlet.
- It signals the client to request the servlet again.
- It specifies the expiration time of the servlet.
The Last-Modified header informs the client about the last modification time of the servlet, allowing the client to cache the response and avoid unnecessary requests if the content hasn't changed.
Bayesian inference is based on the principle of updating the ________ probability based on new data.
- joint
- marginal
- posterior
- prior
Bayesian inference works by updating the prior probability based on new data. This updated probability is known as the posterior probability.
What is the significance of descriptive statistics in data science?
- To create databases
- To describe, show, or summarize data in a meaningful way
- To make inferences about data
- To organize data in a logical way
Descriptive statistics play a significant role in data science as they allow us to summarize and understand data at a glance. They offer simple summaries about the data sample, such as central tendency (mean, median, mode), dispersion (range, variance, standard deviation), and distribution. They help in providing insights into the data, recognizing patterns and trends, and in making initial assumptions about the data. Graphical representation methods like histograms, box plots, bar charts, etc., associated with descriptive statistics, help in visualizing data effectively.
What potential issues can arise from having outliers in a dataset?
- Outliers can increase the value of the mean
- Outliers can lead to incorrect assumptions about the data
- Outliers can make data analysis easier
- Outliers can make the data more diverse
Outliers, which are extreme values that deviate significantly from other observations in the data, can cause serious problems in statistical analyses. They can affect the mean value of the data and distort the overall distribution, leading to erroneous conclusions or predictions. In addition, they can affect the assumptions of the statistical methods and reduce the performance of statistical models. Hence, it's essential to handle outliers appropriately before data analysis.
What type of error can occur if the assumptions of the Kruskal-Wallis Test are not met?
- Either Type I or Type II error
- No error
- Type I error
- Type II error
Violation of the assumptions of the Kruskal-Wallis Test can lead to either Type I or Type II errors. This means you may incorrectly reject or fail to reject the null hypothesis.
In the context of Configuration Management, _____ ensures that any changes made are documented, approved, and reversible.
- Change Management
- Continuous Integration
- Quality Assurance
- Version Control
In the context of Configuration Management, Change Management ensures that any changes made to the system or software are documented, approved through a formal process, and reversible, minimizing the risk of adverse impacts.
Which programming paradigm emphasizes immutability and first-class functions?
- Functional Programming
- Logical Programming
- Object-Oriented Programming
- Procedural Programming
Functional programming is a paradigm that emphasizes immutability and first-class functions. Immutability ensures that data remains constant, and first-class functions allow functions to be treated as first-class citizens.