A negative value of skewness indicates that the distribution is skewed to the ________.
- Left
- Middle
- Right
- nan
A negative value of skewness indicates that the distribution is skewed to the left, meaning that the left tail of the distribution is longer or fatter than the right tail.
Explain the concept of conditional independence in probability theory.
- It is another term for mutual exclusivity
- It means that the independence of two events does not depend on the occurrence of any other events
- It means that two events are independent only when a third event does not occur
- It means that two events are independent only when a third event occurs
Conditional independence in probability theory refers to a situation where two events are independent given the occurrence of a third event. Mathematically, two events A and B are conditionally independent given a third event C if the probability of the intersection of A and B given C is the product of the probabilities of A given C and B given C.
What does the likelihood in Bayes' theorem represent?
- The posterior probability of the event
- The prior probability of the event
- The probability of the event given the evidence
- The probability of the evidence given the event
The likelihood in Bayes' theorem represents the probability of the evidence given the event. It quantifies the extent to which the evidence supports the event.
In polynomial regression, overfitting can occur when the degree of the polynomial is excessively ________.
- High
- Low
- Middle
- Zero
Overfitting can occur when the degree of the polynomial is excessively high. Overfitting refers to a situation where a model is too complex and captures not just the underlying pattern but also the noise in the data. A high-degree polynomial may fit the training data very well, but it may perform poorly on new, unseen data.
A ________ is a smaller group selected from the population of interest.
- distribution
- parameter
- population
- sample
In statistics, a sample is a smaller group or subset that is selected from the population of interest. It's a subset of the population that is used to represent the entire group as a whole. For example, if the population is all people living in a city, a sample might be 1,000 individuals selected randomly from that city.
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 is model selection in the context of multiple regression?
- It is the process of choosing the model with the highest R-squared value.
- It is the process of choosing the most appropriate regression model for the data.
- It is the process of selecting the dependent variable.
- It is the process of selecting the number of predictors in the model.
Model selection refers to the process of choosing the most appropriate regression model for the data among a set of potential models.
The _______ is the simplest measure of dispersion, calculated as the difference between the maximum and minimum values in a dataset.
- Mean
- Range
- Standard Deviation
- Variance
The range is the simplest measure of dispersion, calculated as the difference between the maximum and minimum values in a dataset. It gives us an idea of how spread out the values are, but it doesn't take into account how the values are distributed within this range.
In cluster analysis, a ________ is a group of similar data points.
- cluster
- factor
- matrix
- model
In cluster analysis, a cluster is a group of similar data points. The goal of cluster analysis is to group, or cluster, observations that are similar to each other.
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.