What is the role of the 'R-squared' value in a multiple linear regression model?
- It represents the correlation between the dependent and independent variables
- It represents the error term in the regression model
- It represents the proportion of variance in the dependent variable that is predictable from the independent variables
- It represents the total variance in the dependent variable
The 'R-squared' value, also known as the coefficient of determination, in a multiple linear regression model represents the proportion of variance in the dependent variable that can be predicted from the independent variables. It ranges from 0 to 1, where a higher value indicates a better fit of the model.
What is the support of a continuous random variable?
- The highest and lowest value of the variable
- The mean value of the distribution
- The set of values that have non-zero probability
- The variance of the distribution
The support of a random variable is the set of values in the range of the variable that have non-zero probability. For a continuous random variable, it's the set of values over which the probability density function is non-zero.
How does sample size affect the accuracy of a statistic?
- Larger samples lead to less accurate statistics
- Larger samples lead to more accurate statistics
- Sample size does not affect the accuracy of a statistic
- The relationship between sample size and statistic accuracy is unpredictable
Larger samples tend to lead to more accurate statistics. The reason is that as we increase the sample size, the sample mean gets closer to the population mean, reducing the standard error. In other words, larger samples provide a better estimate of the population parameters, leading to more accurate and reliable results. However, this doesn't mean larger samples are always feasible or more effective, as they require more resources and time.
In simple linear regression, the assumption that the variance of the errors is constant across all levels of the independent variables is known as ________.
- autocorrelation
- heteroscedasticity
- homoscedasticity
- multicollinearity
In statistics, homoscedasticity (or homoskedasticity) is the assumption that the variance of the errors is constant across all levels of the independent variables. This is an important assumption in regression models, including simple linear regression.
Which method is commonly used for session tracking in servlets?
- doGet()
- doPost()
- getSession()
- init()
The getSession() method is commonly used for session tracking in servlets. It returns the current session associated with the request or creates a new session if one does not exist.
What is primarily stored in ServletConfig?
- Context attributes
- Request parameters
- Servlet parameters
- Session data
ServletConfig primarily stores servlet parameters, which are initialization parameters for a servlet.
Which method is used to read form data sent via POST request in a servlet?
- request.getFormData()
- request.getParameter()
- request.readParameter()
- request.readPostData()
The request.readPostData() method is used to read form data sent via POST request in a servlet.
To redirect the response to another resource, the __________ method is used in servlets.
- forward()
- forwardResponse()
- redirect()
- sendRedirect()
The sendRedirect() method is used to redirect the response to another resource in servlets.
Which method is used to set a response header with a String value in a servlet?
- addHeader(String name, String value)
- appendHeader(String name, String value)
- setHeader(String name, String value)
- writeHeader(String name, String value)
The setHeader(String name, String value) method is used to set a response header with a String value in a servlet.
Describe the difference between session cookies and persistent cookies.
- Persistent cookies are often used for user authentication
- Persistent cookies are temporary and expire after the browser is closed
- Session cookies are stored permanently on the client-side
- Session cookies expire after a specified time
Session cookies are temporary and expire when the browser is closed, while persistent cookies are stored on the client-side for a longer duration, typically with an expiration date set by the server.