📗 [1 points] (SU23FQ29, S22FQ17, F22FQ12) df has 5 columns and 10 rows. After applying p = PCA(3) and p.fit(df), what is the shape of p.components_? Note: the rows of p.components_ are the principal components.

📗 [1 points] (SU23FQ28, F21FQ3) The following is the explained_variance_ratio_ of a PCA model: array([0.4, 0.3, 0.2, 0.1]). How many components (at least) do we need to explain 80 percent (or more) of the variance of the original data? 

📗 [1 points] (SU23FQ27, S23FQ6, F21FQ20) Given points [1, 2, 3, 4] and starting centroids [0] and [5], what are the centroids after the first iteration of assigning points and updating centroids, using the iterative K-Means Clustering algorithm with Manhattan distance?

📗 [1 points] (SU23FQ26, F22FQ16, F21FQ9) Which of the following is the best for K Means algorithm?

📗 [1 points] (SU23FQ25, S22FQ4, F21FQ15) Which of the following machine learning algorithm will produce a dendrogram?

📗 [1 points] (S23FQ19) Which of the following does NOT describe a dendrogram? (A dendrogram is not always a ...?)

📗 [1 points] (S23FQ1) Consider the following code for PCA, which of the following approximately reconstructs the original dataframe df using the first three components? p = PCA() then W = p.fit_transform(df) and C = p.components_. 

📗 [1 points] (S23FQ15, S22FQ19, F21FQ18) Which of the following machine learning algorithms enables us to predict a number?

📗 [1 points] (new) The gradient vector dw at [w1, w2, w3, w4] = [1, -1, 2, -2] is [-2, 2, -1, 1], if gradient descent w = w - alpha * dw is used, which variable will increase by the largest amount in the next iteration?

📗 [1 points] (new) If the linear program max 2 w1 - w2 subject to w1 - w2 <= 1 and w1 + w2 >= 0 with w1, w2 >= 0 is written in the standard form max c * x subject A x <= b and x >= 0, what is the matrix A? Assume c = [2, -1] and b = [1, 0].