Principal Component Analysis (PCA) is a technique that reduces dimensionality by creating new uncorrelated variables called _______. These new variables retain most of the variability in the original dataset.
- Eigenvalues
- Eigenvectors
- Factors
- Principal components
Principal Component Analysis (PCA) is a technique that reduces dimensionality by creating new uncorrelated variables called principal components. These new variables retain most of the variability in the original dataset. PCA works by projecting the original data onto a new space, represented by the principal components, which are orthogonal to each other and thus uncorrelated.
How does the missing data mechanism affect the effectiveness of multiple imputation?
- Affects only if data is missing at random
- Affects only if data is not missing at random
- Doesn't affect
- Significantly affects
The missing data mechanism significantly affects the effectiveness of multiple imputation. If data is missing completely at random (MCAR), any method would give unbiased results, but if data is not missing at random (NMAR), the results might be biased even with multiple imputation. The effectiveness also depends on how accurately the imputation model reflects the data process.
What are some factors to consider when choosing between a scatter plot, pairplot, correlation matrix, and heatmap?
- Just the number of variables
- Just the type of data
- Number of variables, Type of data, Audience's familiarity with the plots, All of these
- Only the audience's familiarity with the plots
Choosing between a scatter plot, pairplot, correlation matrix, and heatmap depends on several factors including: the number of variables you want to visualize, the type of data you're working with, and the level of familiarity your audience has with these types of plots.
What information is needed to calculate a Z-score for a particular data point?
- Only the mean of the dataset
- Only the standard deviation of the dataset
- The mean and standard deviation of the dataset
- The median and interquartile range of the dataset
To calculate a Z-score for a particular data point, you need to know the mean and standard deviation of the dataset. The Z-score is calculated by subtracting the mean from the data point and then dividing by the standard deviation.
How does the Variance Inflation Factor (VIF) quantify the severity of Multicollinearity in a regression analysis?
- By calculating the square root of the variance of a predictor.
- By comparing the variance of a predictor to the variance of the outcome variable.
- By measuring how much the variance of an estimated regression coefficient is increased due to multicollinearity.
- By summing up the variances of all the predictors.
VIF provides a measure of multicollinearity by quantifying how much the variance of an estimated regression coefficient increases if predictors are correlated. If the predictors are uncorrelated, the VIF of each variable will be 1. The higher the value of VIF, the more severe the multicollinearity.
What is the first step in the Exploratory Data Analysis process?
- Concluding
- Exploring
- Questioning
- Wrangling
The first step in the EDA process is questioning, i.e., defining the questions that the analysis aims to answer based on the problem's context and data available.
Imagine you're working with a dataset where the standard deviation is very small. How might this impact the effectiveness of z-score standardization?
- It will make the z-score standardization more effective
- It will not affect the z-score standardization
- The scaled values will be very large due to the small standard deviation
- The scaled values will be very small due to the small standard deviation
Z-score standardization scales data by subtracting the mean and dividing by the standard deviation. If the standard deviation is very small, the result of this division could be very large, leading to scaled values that are quite large.
Which outlier detection method is less sensitive to extreme values in a dataset?
- IQR method
- Standard deviation method
- Z-score method
- nan
The IQR (Interquartile Range) method is less sensitive to extreme values as compared to the z-score method or the standard deviation method. This is because IQR is a measure of statistical dispersion, being equal to the difference between upper and lower quartiles.
The detection of outliers using histograms can be influenced by the choice of _________.
- axis scale
- bin size
- color
- orientation
The choice of bin size in a histogram can influence the detection of outliers. If the bins are too wide, outliers may not be visible, while if they're too narrow, normal variation in the data may appear as outliers.
What role does EDA play in formulating hypothesis or model selection in data analysis?
- All of the mentioned
- It assists in defining the variables to be used in the model
- It enables an understanding of the relationships among the variables
- It helps in determining the type of model to apply
EDA plays a fundamental role in hypothesis formulation and model selection. It can guide the choice of the most suitable models based on the understanding of data structure and relationships between variables. It helps define the variables to use in the model, identify potential outliers, detect multicollinearity, and assess the need for variable transformation or creation. Therefore, EDA forms the foundation for further statistical or machine learning analysis.