If a null hypothesis is rejected, what can we infer about the alternative hypothesis?
- It has no relation to the null hypothesis
- It is likely to be true
- It is rejected as well
- It needs to be tested separately
If a null hypothesis is rejected, it means that the alternative hypothesis is likely to be true. We can infer that there's enough evidence in our data to support the claim of the alternative hypothesis.
The Breusch-Pagan test and the White test are common methods to detect __________ in the residuals.
- Autocorrelation
- Heteroscedasticity
- Multicollinearity
- Outliers
The Breusch-Pagan test and the White test are common methods used to detect heteroscedasticity in the residuals. Heteroscedasticity refers to the circumstance in which the variability of a variable is unequal across the range of values of a second variable that predicts it.
How does the Akaike Information Criterion (AIC) handle the trade-off between goodness of fit and model complexity in model selection?
- It always prefers a more complex model.
- It always prefers a simpler model.
- It does not consider model complexity.
- It penalizes models with more parameters to avoid overfitting.
The AIC handles the trade-off by introducing a penalty term for the number of parameters in the model. This discourages overfitting and leads to a balance between model fit and complexity.
What information does a box plot provide about a dataset?
- The correlation between variables
- The exact values of all data points
- The mean and standard deviation
- The minimum, first quartile, median, third quartile, and maximum
A box plot (also known as a whisker plot) displays a summary of the distribution of data values, including the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. The 'box' represents the interquartile range (the distance between Q1 and Q3), and the 'whiskers' represent the range of the data. Outliers may also be plotted as individual points.
Why is sampling without replacement often used in practice?
- It allows for the inclusion of every individual in the population
- It ensures that each selection is independent
- It guarantees that each sample is unique
- It is easier than sampling with replacement
Sampling without replacement is often used in practice because it guarantees that each sample is unique. This means that once an individual is selected, it cannot be chosen again for the same sample. This method can help reduce bias and ensure a more diverse and representative sample.
Why is the Spearman rank correlation considered a non-parametric test?
- It assumes a normal distribution
- It can't handle ordinal data
- It does not assume a normal distribution
- It tests for a linear relationship
The Spearman rank correlation is considered a non-parametric test because it does not assume a normal distribution of data. It only assumes that the variables are ordinal or continuous and that the relationship between them is monotonic.
What are the degrees of freedom in a Chi-square test for a 2x3 contingency table?
- 2
- 3
- 4
- 6
In a Chi-square test, the degrees of freedom for a 2x3 contingency table is (2-1) * (3-1) = 2.
The process that aims to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables is called _______.
- correlation analysis
- covariance analysis
- factor analysis
- regression analysis
The process that aims to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables is called factor analysis.
If the Kruskal-Wallis H test is significant, it is often followed up with ________ to find which groups differ.
- ANOVA
- correlation analysis
- post hoc tests
- t-tests
If the Kruskal-Wallis H test is significant, it is often followed up with post hoc tests to find which groups differ. These tests are used to make pairwise comparisons between groups.
What are the implications of autocorrelation in the residuals of a regression model?
- It causes bias in the parameter estimates
- It indicates that the model is overfit
- It suggests that the model is underfit
- It violates the assumption of independent residuals
Autocorrelation in the residuals of a regression model violates the assumption of independent residuals. This can lead to inefficient estimates and incorrect standard errors, leading to unreliable hypothesis tests and confidence intervals.