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.
How can you test the assumption of independence in a Chi-square test for goodness of fit?
- By calculating the standard deviation of the observations
- By conducting a separate Chi-square test of independence
- By conducting a t-test
- By examining the correlation between observations
To test the assumption of independence in a Chi-square test for goodness of fit, you can conduct a separate Chi-square test of independence. This test compares the observed frequencies in each category with what we would expect if the variables were independent.
How does skewness affect the relationship between the mean, median, and mode of a distribution?
- Changes the relationship
- Increases the standard deviation
- No effect
- Reduces the kurtosis
Skewness affects the relationship between the mean, median, and mode. In a positively skewed distribution, the mean is usually greater than the median, which is greater than the mode. In a negatively skewed distribution, the mode is usually greater than the median, which is greater than the mean.
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.
How can a Chi-square test for independence be used in feature selection?
- It can identify the features that are independent from the target variable
- It can identify the features that are most correlated with the target variable
- It can identify the features that have a significant association with the target variable
- It can identify the features that have the highest variance
A Chi-square test for independence can be used in feature selection by identifying the features that have a significant association with the target variable.