What are the strategies to address the issue of overfitting in polynomial regression?
- Add more independent variables
- Increase the degree of the polynomial
- Increase the number of observations
- Use regularization techniques
Overfitting in polynomial regression can be addressed by using regularization techniques, such as Ridge or Lasso, which add a penalty term to the loss function to constrain the magnitude of the coefficients, resulting in a simpler model. Other strategies can include reducing the degree of the polynomial or using cross-validation to tune the complexity of the model.
When are non-parametric statistical methods most useful?
- When the data does not meet the assumptions for parametric methods
- When the data follows a normal distribution
- When the data is free from outliers
- When there is a large amount of data
Non-parametric statistical methods are most useful when the data does not meet the assumptions for parametric methods. For example, if the data does not follow a normal distribution, or if there are concerns about outliers or skewness, non-parametric methods may be appropriate.
What does a Pearson Correlation Coefficient of +1 indicate?
- No correlation
- Perfect negative correlation
- Perfect positive correlation
- Weak positive correlation
A Pearson correlation coefficient of +1 indicates a perfect positive correlation. This means that every time the value of the first variable increases, the value of the second variable also increases.
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.
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 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.
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 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.
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.
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.