In the context of probability distributions, what is a random variable?
- A variable that always takes a constant value
- A variable that does not have a specific value
- A variable that is not influenced by other variables
- A variable whose outcome is based on the result of a random event
A random variable is a variable whose possible values are outcomes of a random event. It can be either discrete (having specific values) or continuous (any value within a certain range).
What are the two subtypes of quantitative data?
- Categorical and Ordinal
- Discrete and Continuous
- Interval and Ratio
- Nominal and Categorical
Quantitative data can be classified into two subtypes: discrete and continuous. Discrete data can only take certain values (like the number of children in a family – 1, 2, 3, etc.) and Continuous data can take any value within a given range or continuum (like height or weight of a person).
How does a probability mass function differ from a probability density function?
- A probability mass function is used for continuous random variables, while a probability density function is used for discrete random variables
- A probability mass function is used for discrete random variables, while a probability density function is used for continuous random variables
- The two terms are interchangeable
- There is no difference between a probability mass function and a probability density function
A probability mass function is used for discrete random variables and gives the probability that a discrete random variable is exactly equal to some value. A probability density function, on the other hand, is used for continuous random variables and gives the density of the variable at a particular value.
What is multicollinearity in the context of multiple regression?
- It refers to the high correlation between at least two independent variables.
- It refers to the linear relationship between each independent variable and the dependent variable.
- It refers to the presence of a linear relationship between the dependent variables.
- It refers to the relationship between the residuals of the regression model.
Multicollinearity refers to the situation in which two or more predictor variables in a regression model are highly correlated.
How can you interpret interaction terms in a multiple linear regression model?
- All of the above
- They represent the change in the slope of one variable for different values of another variable
- They represent the combined effect of two variables on the response
- They represent the effect of a variable at different levels of another variable
Interaction terms represent the combined effect of two predictors on the response variable. They can also be interpreted as the effect of a predictor at different levels of another predictor or the change in the slope of one predictor for different values of another predictor.
What type of data represents measurements or counts?
- Categorical data
- Nominal data
- Qualitative data
- Quantitative data
Quantitative data represents measurements or counts. It can be mathematically quantified and is usually collected in numerical form. For example, data such as age, weight, height, and number of items are all quantitative data.
How does the Mann-Whitney U test handle ties?
- Ties are given the average rank
- Ties are given the highest rank
- Ties are given the lowest rank
- Ties are removed from the data
In the Mann-Whitney U test, ties (equal values) are handled by giving them the average of the ranks they would have received if they were not tied.
In the presence of ties or zeros in differences, it's usually better to apply _________ test.
- Mann-Whitney U
- Sign
- Wilcoxon Signed Rank
- nan
In the presence of ties or zeros in differences, it's usually better to apply the Sign Test because the Wilcoxon Signed Rank Test discards zeros and the Sign Test is less sensitive to ties than other tests.
When is it more appropriate to use the Wilcoxon Signed Rank Test rather than the Sign Test?
- When data is nominal
- When data is normally distributed
- When data is ordinal or interval
- When sample size is large
The Wilcoxon Signed Rank Test is more appropriate to use when data is ordinal or interval because it takes into account the magnitude of the differences between paired observations, unlike the Sign Test which only considers the sign of the differences.
The Mann-Whitney U test can be used when the assumptions of the ________ test are not met.
- ANOVA
- F
- chi-square
- t
The Mann-Whitney U test can be used as an alternative when the assumptions of the t-test (e.g., normality, homogeneity of variance) are not met.
What does probability measure?
- Degree of difference between groups
- Likelihood of an event occurring
- Speed of an event
- Strength of a relationship
Probability measures the likelihood or chance of an event occurring. It is a mathematical concept that is fundamental to statistics and data science, helping to predict outcomes and guide decision-making.
If a dataset has positive skewness, where would you find the majority of the data values?
- At the mean
- It is equally distributed
- To the left of the mean
- To the right of the mean
If a dataset has positive skewness, the majority of the data values are found to the left of the mean. The distribution will have a longer or fatter tail on the right side.