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.
What is the key characteristic of a symmetric distribution?
- It has a mean of zero
- It has a mode at the peak
- It has no outliers
- It has the same shape on the left and right when split vertically at the center
The key characteristic of a symmetric distribution is that it has the same shape on the left and right when split vertically at the center (i.e., about the mean). This means that the frequencies of corresponding values on either side of the center are equal.
The measure of how much individual sample means will vary is called the __________ error.
- Absolute
- Margin of
- Sampling
- Standard
The standard error of a statistic is a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates. It is used to test hypotheses on the grounds of a set of data. For sample means, the standard error tells us how the mean varies from one sample to another.
How does changing the units of measurement affect the standard deviation and variance of a dataset?
- It decreases them
- It depends on the new units
- It doesn't affect them
- It increases them
Changing the units of measurement will change the scale of the data, and hence will affect the values of standard deviation and variance. If the data is scaled up, both measures will increase, and if the data is scaled down, they will decrease. However, the relative dispersion, as measured by the coefficient of variation, will remain the same.
If the p-value from a Mann-Whitney U test is less than the significance level, you would ________ the null hypothesis.
- accept
- either accept or reject
- fail to reject
- reject
If the p-value from a Mann-Whitney U test is less than the significance level (often 0.05), you would reject the null hypothesis, suggesting there is a significant difference between the groups.
What does the Law of Large Numbers state?
- It states that as the size of a sample is increased, the mean value of the sample will get closer to the mean or expected value of the population.
- It states that if an event is repeated under identical conditions, the probability of the event remains the same.
- It's a rule which states that the sum of the probabilities of all possible events is 1.
- It's the law that states the probability of an event is always constant.
The Law of Large Numbers states that as a sample size grows, its mean gets closer to the average of the whole population. In other words, as the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.
The graphical representation of residuals versus predicted values is known as a ________ plot.
- Box
- Histogram
- Residual
- Scatter
A Residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.
What can the Mann-Whitney U test tell you about the shape of your distributions?
- It can confirm if your distributions are normal
- It can confirm if your distributions are skewed
- It can confirm if your distributions have equal variances
- It cannot tell you anything about the shape of your distributions
The Mann-Whitney U test does not provide information about the shape of the distributions. It is a non-parametric test that does not make any assumptions about the distribution of the data.