When is it appropriate to use polynomial regression?
- When the dependent variable is categorical
- When the relationship between variables is linear
- When the relationship between variables is non-linear
- When there is no relationship between variables
Polynomial regression is appropriate when the relationship between variables is non-linear. It allows for modeling of relationships that change in direction at different levels of the independent variables, which can be useful when dealing with complex data sets that do not follow a simple linear relationship.
The null hypothesis for the Kruskal-Wallis Test states that all ________ have the same distribution.
- factors
- groups
- pairs
- variables
The null hypothesis for the Kruskal-Wallis Test states that all groups have the same distribution. It tests whether samples originate from the same distribution.
How does the correlation coefficient change when you switch the X and Y variables?
- It changes sign
- It decreases
- It increases
- It remains the same
The correlation coefficient remains the same when you switch the X and Y variables. This is because correlation measures the strength and direction of a relationship between two variables, not the dependency of one on the other.
What is meant by the term "multicollinearity" in multiple linear regression?
- The dependent variables are correlated with each other
- The error terms are correlated with each other
- The independent variables are correlated with each other
- The residuals are correlated with each other
In multiple linear regression, multicollinearity refers to a situation in which two or more independent variables are highly linearly related. This can cause problems because it can affect the interpretability of the regression coefficients and can make the model unstable.
How do we define expectation of a random variable?
- It is the most likely outcome of the variable
- It is the range of the variable
- It is the variance of the variable
- It is the weighted average of all possible values the variable can take, with weights being the respective probabilities
The expected value or expectation of a random variable is a key concept in probability and statistics and represents the weighted average of all possible values that the variable can take, with weights being the respective probabilities.
When is it appropriate to use quantitative data over qualitative data?
- Never
- When both measuring and categorizing are required
- When categorizing or describing is required
- When measuring or counting is required
Quantitative data is appropriate to use when measuring or counting is required, or when the data can be numerically quantified. This data type allows for statistical analysis and can provide a more objective and precise understanding than qualitative data. For example, it's appropriate to use quantitative data when you want to know how many people visited a website, how much customers are willing to pay for a product, or how often a certain event occurs.
What kind of hypothesis is tested in the Sign Test?
- The means of two groups are equal
- The medians of two groups are equal
- The proportions of two groups are equal
- The variances of two groups are equal
The Sign Test tests the null hypothesis that the medians of two groups are equal.
PCA assumes that the data follows a _______ distribution.
- Poisson
- binomial
- normal
- uniform
PCA makes the assumption that the data follows a multivariate normal distribution. This means that all linear combinations of the original variables also follow a normal distribution.
How does the concept of conditional probability relate to the Multiplication Rule?
- Conditional probabilities are the inverse of the Multiplication Rule
- The Multiplication Rule calculates conditional probabilities
- The Multiplication Rule can be rewritten using conditional probabilities
- They are unrelated concepts
Conditional probability and the Multiplication Rule are interconnected. The Multiplication Rule can be rewritten using conditional probabilities. Specifically, the Multiplication Rule states that the probability of two events A and B occurring (P(A ∩ B)) equals the probability of A given B (P(A
A ________ ANOVA is used when we want to compare more than two groups, and we have one categorical variable.
- Factorial
- One-way
- Three-way
- Two-way
A one-way ANOVA is used when we want to compare more than two groups, and we have one categorical variable. The 'one-way' refers to one independent variable or factor.