Probability and Statistics Quiz

Decision Trees

• Decision tree models are built using DecisionTreeClassifier or DecisionTreeRegressor.
• Gini Index does not enforce the resulting tree to have multiway splits.
• Chance nodes are represented by circles.
• Entropy is the measure of uncertainty of a random variable, characterizing the impurity of an arbitrary collection of examples.
• End nodes are represented by squares.
• Decision tree learners may create biased trees if some classes dominate, and the solution is to balance the dataset prior to fitting.

Statistics

• A standard normal distribution has a mean of 0 and a standard deviation of 1.
• The area to the left of the mean in a standard normal probability distribution is 0.5.
• The probability of a player weighing more than 241.25 pounds in a normal distribution with a mean of 200 pounds and a standard deviation of 25 pounds is 0.0495.
• The probability of a player weighing less than 250 pounds in the same distribution is 0.9772.

Probability

• Two events having non-zero probabilities cannot be both mutually exclusive and independent.
• A normal distribution with a standard deviation of 1 and a mean of 0 is a standard normal distribution.

Regression Analysis

• The coefficient of determination (R-squared) varies from 0 to 1.
• In a regression analysis, the null hypothesis is rejected if the p-value is less than the significance level.
• A 95% confidence interval for B1 can be calculated to test hypotheses.

Data Analytics

• The variance of error is not the same for all values of the independent variable.
• The interval estimate of the mean value of y (dependent variable) for a given value of x is defined as the predicted value of y plus or minus the margin of error.
• The formula for dissimilarity computation between two objects for categorical variables is D(i, j) = p-m / p.

Clustering

• Std deviation (std_f) and mean absolute deviation (s_f) are not equally affected by outliers in a dataset.
• Standardizing the data is beneficial during clustering analysis.
• Possible termination conditions in K-Means include a fixed number of iterations, no change in assignment of observations to clusters between iterations, and no change in centroids between successive iterations.
• Hierarchical clustering uses a merging approach.
• Hierarchical clustering should primarily be used for exploration.
• Average-link is not the only metric used for finding dissimilarity between two clusters in hierarchical clustering.
• K-means clustering is sensitive to the correlation between variables.

CART Model

• CART is a supervised learning technique.
• CART adopts a greedy approach.
• CART is suitable for building decision trees.

Clustering Algorithms

• K-means clustering works well when the shape of the clusters is hyperspherical.
• Agglomerative Hierarchical clustering and Divisive Hierarchical clustering are suitable for building hierarchical clusters.