How does factor analysis differ from principal component analysis (PCA)?
- Factor analysis does not involve rotation of variables, while PCA does
- Factor analysis looks for shared variance while PCA looks for total variance
- PCA focuses on unobservable variables, while factor analysis focuses on observable variables
- PCA is used for dimensionality reduction, while factor analysis is used for data cleaning
Factor analysis and PCA differ primarily in what they seek to model. Factor analysis models the shared variance among variables, focusing on the latent or unobservable variables, while PCA models the total variance and aims at reducing the dimensionality.
How would an outlier affect the confidence interval for a mean?
- It would make the interval narrower
- It would make the interval skewed
- It would make the interval wider
- It would not affect the interval
An outlier can significantly affect the mean and increase the variability in the data, which would lead to a larger standard error and thus a wider confidence interval.
What is the difference between descriptive and inferential statistics?
- Descriptive and inferential statistics are the same
- Descriptive statistics predict trends; inferential statistics summarize data
- Descriptive statistics summarize data; inferential statistics make predictions about the population
- Descriptive statistics summarize data; inferential statistics visualize data
Descriptive statistics provide simple summaries about the sample and the measures. It's about describing the collected data using the measures such as mean, median, mode, etc. On the other hand, inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn. It is the process of using data analysis to deduce properties of an underlying distribution of probability.
Non-parametric tests are also known as ________ tests because they make fewer assumptions about the data.
- assumption-free
- distribution-free
- free-assumption
- free-distribution
Non-parametric tests are also known as distribution-free tests because they make fewer assumptions about the data, specifically, they do not require the data to follow a specific distribution.
What is the difference between a parameter and a statistic in the field of statistics?
- A parameter and a statistic are the same thing
- A parameter is based on a sample; a statistic is based on the population
- A statistic is a numerical measure; a parameter is a graphical representation
- A statistic is based on a sample; a parameter is based on the population
In the field of statistics, a parameter is a numerical characteristic of a population, whereas a statistic is a numerical characteristic of a sample. Parameters are often unknown because we cannot examine the entire population. We use statistics, which we compute from sample data, to estimate parameters.
How does adding more predictors to a multiple linear regression model affect its inferences?
- It always improves the model
- It always makes the model worse
- It can lead to overfitting
- It has no effect on the model
Adding more predictors to a model may increase the R-squared value, making it appear that the model is improving. However, if these additional predictors are not truly associated with the response variable, it may result in overfitting, making the model perform poorly on new, unseen data.
How does ridge regression help in dealing with multicollinearity?
- By eliminating the correlated variables.
- By increasing the sample size.
- By introducing a penalty term to shrink the coefficients.
- By transforming the variables.
Ridge regression introduces a regularization term (penalty term) into the loss function which helps to shrink the coefficients towards zero and mitigate the effect of multicollinearity.
Which mathematical concept is at the core of PCA?
- Differentiation
- Eigenvalues and Eigenvectors
- Integration
- Matrix Multiplication
PCA relies heavily on the concepts of Eigenvalues and Eigenvectors. These allow it to determine the axes along which the data has the most variance, which are used to form the new variables (principal components).
___________ refers to the condition where the variance of the errors or residuals is constant across all levels of the explanatory variables.
- Autocorrelation
- Heteroscedasticity
- Homoscedasticity
- Multicollinearity
Homoscedasticity is the condition in which the variance of the errors or residuals is constant across all levels of the explanatory variables. It is one of the key assumptions of linear regression.
A Type II error occurs when we fail to reject the null hypothesis, even though it is _______.
- FALSE
- Not applicable
- Not proven
- TRUE
A Type II error occurs when we fail to reject the null hypothesis, even though it is false. This is also known as a "false negative" error.