What is the shape of a normal distribution?
- Skewed to the left
- Skewed to the right
- Symmetrical bell curve
- Uniform flat shape
The normal distribution, also known as Gaussian distribution, is a continuous probability distribution that has a bell-shaped curve. It is symmetrical around its mean, implying that the data near the mean are more frequent in occurrence than data far from the mean.
How can multicollinearity be addressed in multiple regression analysis?
- By adding more variables to the model.
- By increasing the sample size.
- By removing one or more of the correlated variables.
- Multicollinearity cannot be addressed.
Multicollinearity can be addressed by removing one or more of the highly correlated independent variables.
Bayes' theorem is a fundamental principle underlying ________ learning.
- active
- machine
- passive
- rote
Bayesian methods, which are grounded in Bayes' theorem, play an integral role in many areas of machine learning. They allow the model to update its predictions as it receives more data, making them particularly useful for tasks involving prediction and recommendation.
What is the purpose of an F-test in multiple linear regression?
- To check for multicollinearity
- To check the linearity of the model
- To check the normality of residuals
- To check the overall significance of the model
The F-test in multiple linear regression is used to test the overall significance of the model, essentially testing whether at least one of the predictors' coefficients is non-zero and hence contributes to explaining the variability in the response variable.
In the context of multiple linear regression, __________ refers to the phenomenon where the coefficients estimate becomes highly sensitive to changes in the model.
- Autocorrelation
- Heteroscedasticity
- Multicollinearity
- Overfitting
Multicollinearity refers to the situation in multiple linear regression where the predictor variables are highly correlated. This can lead to unstable estimates of the coefficients which can change erratically in response to small changes in the model.
What is the purpose of an interaction term in a regression model?
- To increase the complexity of the model
- To minimize the error of the model
- To represent the combined effect of two variables
- To represent the effect of one variable based on the level of another
An interaction term in a regression model is used to represent the combined effect of two independent variables on the dependent variable. It captures situations where the effect of one variable on the dependent variable is different at different levels of another variable.
In what type of problem scenarios is Bayes' Theorem most commonly used?
- When new evidence is used to update the probability of an event
- When the data is categorical
- When the events are mutually exclusive
- When the population is normally distributed
Bayes' Theorem is most commonly used when new evidence is used to update the probability of an event. It provides a way to revise existing predictions or theories (prior probabilities) in light of new data (the likelihood).
Which type of data can be categorized into groups: qualitative or quantitative?
- Both
- None
- Qualitative
- Quantitative
Qualitative data can be categorized into groups. It represents characteristics or attributes and is often categorized or grouped. For example, hair color (blonde, brunette, etc.) or marital status (single, married, etc.) are qualitative data.
The ________ is the middle value in a data set when the data is arranged in ascending or descending order.
- Mean
- Median
- Mode
- nan
The median is the value separating the higher half from the lower half of a data sample. If the data set has an odd number of observations, the number in the middle is the median. If there is an even number of observations, the median is defined as the arithmetic mean of the two middle values.
The probability of the intersection of Events A and B is represented by _______.
- P(A + B)
- P(A - B)
- P(A ∩ B)
- P(A ∪ B)
The probability of the intersection of Events A and B is represented by P(A ∩ B), which means the probability that both events A and B occur.