In the presence of multicollinearity, the estimated regression coefficients are _______.
- biased
- equal to zero
- negative
- unbiased
Even in the presence of multicollinearity, the least squares estimates of the regression coefficients are still unbiased. However, they are less precise and have high standard errors.
How does standard deviation differ from the mean absolute deviation?
- Mean absolute deviation is always greater
- Standard deviation is always greater
- Standard deviation squares the deviations while mean absolute deviation takes absolute values
- They are the same
The standard deviation and mean absolute deviation both measure the dispersion in a dataset. The key difference lies in how they treat deviations from the mean: standard deviation squares the deviations before averaging them, while mean absolute deviation takes the absolute value of deviations before averaging. As a result, standard deviation is more sensitive to extreme values than the mean absolute deviation.
Quantitative data represents quantities and can be measured on a ________ scale.
- Categorical
- Nominal
- Numerical
- Ordinal
Quantitative data represents quantities and can be measured on a Numerical scale. It includes both discrete data (e.g., the number of students in a class) and continuous data (e.g., the weight of a person).
What is the purpose of Pearson's Correlation Coefficient?
- To compute the standard deviation of a dataset
- To determine the linear relationship between two variables
- To find the mean of a set of values
- To transform qualitative data into quantitative data
Pearson's correlation coefficient (denoted as r) is a measure of the strength and direction of association that exists between two continuous variables. It measures the degree to which pairs of data for these two variables lie on a line. The values lie between -1 and 1, where 1 indicates a perfect positive correlation, -1 a perfect negative correlation, and 0 no correlation at all.
If the population standard deviation is unknown, we use the sample standard deviation to estimate the ________ of the mean.
- Confidence interval
- Range
- Standard error
- Variability
If the population standard deviation is unknown, the sample standard deviation is used to estimate the standard error of the mean. The standard error is a measure of how much the sample mean is expected to vary from the true population mean.
In ANOVA, if the F statistic is significantly high, it suggests that the null ________ should be rejected.
- Distribution
- Hypothesis
- Model
- Theory
If the F statistic in an ANOVA is significantly high, it suggests that the null hypothesis should be rejected. The null hypothesis in ANOVA is typically that all group means are equal.
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.
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 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.