Why is it important to check the normality of residuals in regression analysis?
- To ensure the accuracy of the model's predictive ability
- To ensure the model is not overfitting
- To make sure the regression line is the best fit
- To satisfy one of the key assumptions of linear regression
It is important to check the normality of residuals in regression analysis because it is one of the key assumptions of linear regression. If the residuals are normally distributed, it validates the model's assumptions and ensures the accuracy of the hypothesis tests and confidence intervals.
Which type of graph is frequently used to represent an estimate of a variable's probability density function?
- Bar chart
- Kernel Density plot
- Pie chart
- Scatter plot
A Kernel Density Plot is frequently used to represent an estimate of a variable's probability density function. This type of plot uses a smoothing kernel to create a curve and the area under the curve is equal to 1.
You are analyzing a data set that includes the number of visitors to a website per day. How would you categorize this data type?
- Continuous data
- Discrete data
- Nominal data
- Ordinal data
The number of visitors to a website per day would be discrete data as it is countable in a finite amount of time.
For data with outliers, the _____ is typically a better measure of central tendency as it is less sensitive to extreme values.
- Mean
- Median
- Mode
- Variance
The "Median" is less sensitive to extreme values, or outliers, in a dataset. Therefore, it's often a better measure of central tendency when outliers are present.
If you are working with a large data set and need to produce interactive visualizations for a web application, which Python library would be the most suitable?
- Bokeh
- Matplotlib
- Plotly
- Seaborn
Plotly is well-suited for creating interactive visualizations and can handle large data sets efficiently. It also supports rendering in web applications, making it ideal for this scenario.
What type of bias could be introduced by mean/median/mode imputation, particularly if the data is not missing at random?
- Confirmation bias
- Overfitting bias
- Selection bias
- Underfitting bias
Mean/Median/Mode Imputation, particularly when data is not missing at random, could introduce a type of bias known as 'Selection Bias'. This is because it might lead to incorrect estimation of variability and distorted representation of true relationships between variables, as the substituted values may not accurately reflect the reasons behind the missingness.
High degrees of Multicollinearity can inflate the _________ of the estimated regression coefficients.
- Bias
- Distribution
- Efficiency
- Variance
High degrees of multicollinearity can inflate the variance of the estimated regression coefficients. This means that the coefficients become highly sensitive to minor changes in the model, which can make them unreliable and difficult to interpret.
You are dealing with a dataset where outliers significantly affect the mean of the distribution but not the median. What approach would you suggest to handle these outliers?
- Binning
- Removal
- Transformation
- nan
In this case, a transformation such as a log or square root transformation might be suitable. These transformations pull in high values, thereby reducing their impact on the mean.
The process of replacing each missing data point with a set of plausible values creating multiple complete data sets is known as ____________.
- Mean Imputation
- Mode Imputation
- Multiple Imputation
- Regression Imputation
This process is called multiple imputation. It generates several different plausible imputed datasets and the results from these are combined to produce the final analysis.
What is the relationship between the Z-score of a data point and its distance from the mean?
- The Z-score is independent of the distance from the mean
- The higher the Z-score, the closer the data point is to the mean
- The higher the Z-score, the further the data point is from the mean
- The lower the Z-score, the further the data point is from the mean
The higher the Z-score, the further the data point is from the mean. A Z-score of 0 indicates that the data point is identical to the mean score.