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Questions and Answers
In linear regression, which of the following is the correct formula for the coefficient of determination ($R^2$)?
In linear regression, which of the following is the correct formula for the coefficient of determination ($R^2$)?
- $R^2 = \frac{SS_{reg}}{SS_{tot}}$
- $R^2 = 1 - \frac{SS_{reg}}{SS_{tot}}$
- $R^2 = 1 - \frac{SS_{reg}}{n-1}$
- $R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$ (correct)
When conducting hypothesis testing, the p-value is:
When conducting hypothesis testing, the p-value is:
- The probability of correctly accepting the null hypothesis
- The probability of incorrectly rejecting the null hypothesis
- The probability of observing a test statistic exactly at the one actually observed
- The probability of observing a test statistic as extreme as, or more extreme than, the one actually observed, assuming that the null hypothesis is true (correct)
In probability theory, the complement rule states that:
In probability theory, the complement rule states that:
- The probability of the intersection of two independent events is equal to the product of their individual probabilities
- The probability of the complement of an event is equal to 1 minus the probability of the event (correct)
- The probability of the intersection of two events is equal to the sum of their individual probabilities minus the probability of their union
- The probability of the union of two events is equal to the sum of their individual probabilities
In exploratory data analysis, which statistical measure is used to describe the dispersion of a dataset?
In exploratory data analysis, which statistical measure is used to describe the dispersion of a dataset?
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When collecting data for a study, what type of sampling method involves dividing the population into non-overlapping subgroups and then taking a simple random sample from each subgroup?
When collecting data for a study, what type of sampling method involves dividing the population into non-overlapping subgroups and then taking a simple random sample from each subgroup?
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In probability theory, if two events are independent, what is the probability of both events A and B occurring?
In probability theory, if two events are independent, what is the probability of both events A and B occurring?
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