(To be done by hand) Exploring his own drink-and-drive habits,a student recalls the last 7 parties that he attended. He records the number of cans of beer he drank, his highway speed on the way home, and whether he was stopped by policeUse the following statistical machine learning methods to predict whether or not the person will be stopped by police.(a) Tree. Draw a decision tree that can be used for this classification task. Label each node in order to make it clear how to use this tree for classification. What is the training error rate of this tree?(b) Prunning. Suppose the tree is pruned to just one split. If “speed" is the only variable used, what split minimizes the Gini idex? What is the Gini index for this split, and what is the training error rate of this tree?(c) Bagging. Four bootstrap samples from the given data are (listed by the party number): Bootstrap sample #1 − (1, 1, 2, 3, 4, 5, 6)Bootstrap sample #2 − (3, 4, 4, 5, 5, 7, 7)Bootstrap sample #3 − (3, 3, 4, 6, 7, 7, 7)Bootstrap sample #4 − (1, 2, 2, 2, 5, 5, 6)Draw a tree based on each bootstrap sample. Predict the out-of-bag data by the majority vote. Use these results to estimate the testing error rate of this method.Problem 2. (10 points)(To be done by hand) Multiple linear regression models are studied for eight different sets of data. Below are various kinds of residual plots. For each case, give a brief dignostics of the regression model and suggest a way to improve the model, if necessary.

Factor the trinomial completely.a. (y - 10)(y - 3)b. (y + 10)(y + 3)c. (y + 10)(y - 3)d. (y - 10)(y + 3)Factor the trinomial completely. a. (6p + 6)(p - 1)b. (2p + 3)(3p - 2)c. (3p + 3)(2p - 2)d. (6p - 1)(p + 6)Factor the polynomial completely. a. b. (9 + 4k)(9 - 4k)c. d. Prime polynomialFactor the polynomial completely.a. (n+6)2b. (n+6)(n-6)c. (n-6)2d. Prime polynomialFactor the trinomial completely.a. 2x(3y - 4)2b. 2(3xy + 4x)2c. 2x(3y + 4)(3y - 4)d. Prime polynomialFactor the polynomial completely.a. (x - 4)(3x - 18)b. 3(x - 4)(x - 6)c. (x + 2)(x - 7)d. (x - 10)(x - 1)Factor the polynomial completely. x4-1a. (x2+1)(x2-1)b. (x2+1(x+1)(x-1)c. (x+1)(x-1)(x+1)(x-1)d. (x2-1)(x+1)(x-1)Factor the polynomial completely.m3 - n3a. (m + n)(m - n)b. (m + n)(m - n)(m - n)c. (m - n)(m2 + mn + n2)d. (m + n)(m2 - mn + n2)Factor the polynomial completely.a3b+8b4a. (a+2b2)(a-2b2)b. b(a+2b)(a2-2ab+4b2)c. Prime polynomiald. b(a+2b)(a2-4ab+4b2)Factor the polynomial completely. (y+2)2-49a. (y + 2)(y - 7)(y + 7)b. (y + 9)(y - 5)c. (y - 9)(y + 5)d. (y - 9)(y + 9)