The ________ score is a measure of how close each point in one cluster is to the points in the neighboring clusters.
- boundary
- distance
- proximity
- silhouette
The silhouette score is a measure of how close each point in one cluster is to the points in the neighboring clusters. It ranges from -1 (incorrect clustering) to +1 (highly dense clustering). 0 indicates overlapping clusters.
What types of scales of measurement are suitable for non-parametric tests?
- Nominal, ordinal, interval, and ratio
- Only interval and ratio
- Only nominal and ordinal
- Only ratio
Non-parametric tests can be used with nominal, ordinal, interval, and ratio scales of measurement. This is one of the reasons why non-parametric tests are sometimes chosen over parametric ones, as they can handle data that are not interval or ratio (which are required for many parametric tests).
In a multiple linear regression model, the assumption that the variance of the residuals is the same for all levels of the predictors is known as __________.
- Autocorrelation
- Homoscedasticity
- Linearity
- Multicollinearity
Homoscedasticity refers to the assumption in regression analysis that the variance of the residuals (or "errors") is constant across all levels of the independent variables.
If the p-value from a Mann-Whitney U test is less than the significance level, you would ________ the null hypothesis.
- accept
- either accept or reject
- fail to reject
- reject
If the p-value from a Mann-Whitney U test is less than the significance level (often 0.05), you would reject the null hypothesis, suggesting there is a significant difference between the groups.
What does the Law of Large Numbers state?
- It states that as the size of a sample is increased, the mean value of the sample will get closer to the mean or expected value of the population.
- It states that if an event is repeated under identical conditions, the probability of the event remains the same.
- It's a rule which states that the sum of the probabilities of all possible events is 1.
- It's the law that states the probability of an event is always constant.
The Law of Large Numbers states that as a sample size grows, its mean gets closer to the average of the whole population. In other words, as the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.
The graphical representation of residuals versus predicted values is known as a ________ plot.
- Box
- Histogram
- Residual
- Scatter
A Residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.
What can the Mann-Whitney U test tell you about the shape of your distributions?
- It can confirm if your distributions are normal
- It can confirm if your distributions are skewed
- It can confirm if your distributions have equal variances
- It cannot tell you anything about the shape of your distributions
The Mann-Whitney U test does not provide information about the shape of the distributions. It is a non-parametric test that does not make any assumptions about the distribution of the data.
What is the purpose of multiple linear regression analysis?
- To classify data into different categories
- To cluster data into different groups
- To examine the relationship between several independent variables and a dependent variable
- To predict the outcome of a binary dependent variable
Multiple linear regression analysis is used to understand the relationship between several independent (explanatory) variables and a dependent (response) variable. It can also be used for predicting the mean value of the dependent variable given the values of the independent variables.
In a 95% confidence interval, if the true population parameter lies outside of the interval, it is considered a _______ error.
- Alpha
- Standard
- Type I
- Type II
In a 95% confidence interval, if the true population parameter lies outside of the interval, it is considered a Type I error. This is when the null hypothesis is true, but is incorrectly rejected.
How does PCA help in reducing the dimensionality of the dataset?
- By creating new uncorrelated variables
- By grouping similar data together
- By removing unnecessary data
- By rotating the data to align with axes
PCA reduces the dimensionality of a dataset by creating new uncorrelated variables that successively maximize variance. These new variables or "principal components" can replace the original variables, thus reducing the data's dimensionality.