What does the slope of the regression line represent in simple linear regression?
- It represents the change in the dependent variable for a one-unit change in the independent variable
- It represents the error term
- It represents the independent variable
- It represents the strength of the correlation
The slope of the regression line in simple linear regression represents the change in the dependent variable for a one-unit change in the independent variable. It quantifies the strength and direction of the linear relationship between the two variables.
The ________ probability in Bayes' theorem is the revised probability of an event occurring after taking into account new information.
- joint
- marginal
- posterior
- prior
In Bayes' theorem, the posterior probability is the revised probability of an event occurring after taking into account new evidence.
What does a 95% confidence interval mean?
- That 95% of the population is within the interval
- That 95% of the sample data lies within the interval
- That the interval captures the true population parameter 95% of the time
- That there is a 95% chance that the interval contains the mean
A 95% confidence interval means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95% of the cases.
The _________ is crucial in hypothesis testing and the construction of confidence intervals.
- Central Limit Theorem
- Law of Large Numbers
- Probability Rule
- Sampling Distribution
The Central Limit Theorem is crucial in hypothesis testing and the construction of confidence intervals. By ensuring the normality of the distribution, it allows us to make inferences about the population from our sample data and to assess the likelihood that our sample mean is a reliable estimate of the population mean.
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.
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.