The _______ Rule is used when we want to find the probability of two events happening at the same time.
- Addition
- Division
- Multiplication
- Subtraction
The Multiplication Rule is used when we want to find the probability of two events happening at the same time. Specifically, it states that the probability of two independent events both occurring is the product of their individual probabilities.
What does skewness measure in a dataset?
- Central tendency
- Dispersion
- Kurtosis
- Symmetry or lack of symmetry
Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values. Negative skewness indicates a distribution with an asymmetric tail extending towards more negative values.
Can a symmetrical distribution have nonzero kurtosis?
- No
- Only if it's a normal distribution
- Only if it's not a normal distribution
- Yes
Yes, a symmetrical distribution can have nonzero kurtosis. Kurtosis is a measure of the weight in the tails, or the extreme values, which can occur in both directions, thus not affecting the symmetry. For example, a normal distribution is symmetric and has a kurtosis greater than zero.
In what scenarios might Spearman's rank correlation coefficient be a better choice than Pearson's?
- When both variables are normally distributed
- When the data contains outliers or is not normally distributed
- When the relationship between variables is linear
- When the relationship between variables is non-linear and non-monotonic
Spearman's rank correlation coefficient is a non-parametric measure of correlation, meaning it can be used when the data is not normally distributed. It is also less sensitive to outliers compared to Pearson's coefficient. Further, it can be used to measure monotonic relationships, whether they are linear or not.
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.
Simple linear regression is a method used to predict a ________ variable using a ________ variable.
- continuous, discrete
- dependent, independent
- discrete, continuous
- independent, dependent
Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables: One variable, denoted x, is regarded as the predictor, explanatory, or independent variable. The other variable, denoted y, is regarded as the response, outcome, or dependent variable.
Can the probability of an event be a negative number?
- It depends on the event
- No
- Only if the event is impossible
- Yes
The probability of an event cannot be a negative number. By definition, the probability of an event is a number between 0 and 1, inclusive.
What is the key characteristic of a symmetric distribution?
- It has a mean of zero
- It has a mode at the peak
- It has no outliers
- It has the same shape on the left and right when split vertically at the center
The key characteristic of a symmetric distribution is that it has the same shape on the left and right when split vertically at the center (i.e., about the mean). This means that the frequencies of corresponding values on either side of the center are equal.