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 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.
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.
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 total probability of all outcomes of an experiment is _______.
- 0
- 0.5
- 1
- It depends on the number of outcomes
The total probability of all outcomes of an experiment is 1. This is a fundamental rule of probability, known as the Law of Total Probability, which states that the sum of the probabilities of all possible outcomes of an experiment is equal to 1.
When the effect of one independent variable on the dependent variable varies with the level of another independent variable, it's known as an ________ effect.
- Additive
- Constant
- Interaction
- Subtractive
This is known as an interaction effect. In the context of regression analysis, an interaction effect occurs when the effect of one independent variable on the dependent variable depends on the value of another independent variable.
What is the difference between the Law of Large Numbers and the Central Limit Theorem?
- Both are essentially the same.
- The Central Limit Theorem is a law, while the Law of Large Numbers is a theorem.
- The Law of Large Numbers is used for calculating probabilities, while the Central Limit Theorem is used for integration.
- The Law of Large Numbers states that as a sample size increases, the sample mean approaches the population mean, while the Central Limit Theorem states that the distribution of sample means approximates a normal distribution as the sample size increases.
The Law of Large Numbers and the Central Limit Theorem are both key concepts in probability and statistics, but they say different things. The Law of Large Numbers states that as the size of a sample is increased, the sample mean will get closer to the population mean. The Central Limit Theorem, on the other hand, states that as the sample size increases, the distribution of sample means approaches a normal distribution.
The Chi-square test for goodness of fit is only applicable to ________ data.
- categorical
- continuous
- normally distributed
- time series
The Chi-square test for goodness of fit is applicable only to categorical data. It is used to determine whether the observed frequencies differ from the expected frequencies.
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.
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.
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.
The process of estimation is made more precise by decreasing the _______ of the confidence interval.
- Confidence level
- Sample size
- Standard error
- Width
The precision of the estimation process increases as the width of the confidence interval decreases. A smaller width implies that the range of values within which the population parameter lies is narrower.