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Q1. The table below gives the number of hours spent studying for an ML exam (x), and the final exam grade (y). x 2 5 1 0 4 2 3 y 77 92 70 63 90 75 84 Find the linear regression model that fits the data and the predicted grade for a student who studied for 6 hours? Q2. The table below represents the relation between prices of houses (y) and their sizes (x_1) in meter square and number of rooms (x_2). X 1 40 50 50 60 100 X 2 1 2 1 2 4 y 100 110 80 120 160 a. Walk through the steps of finding a linear regression model that fits the data in a closed form expression. Define the objective function and the way you solve it to yields the final closed form solution. b. Compute the predicted price of a house of size 80m and has 3 bedrooms? c. Find the updated value of the model after performing each GD iteration for total of 3 iterations if the learning rate a = 0.001, and = [1,0.5,0]. Q3. Suppose you trained a logistic regression classifier, and your hypothesis is: fg = g(o +1x1 + Bx2) Plot the decision boundary of this classifier when: a. Bo 5. =0, = -1. b. Bo = -4,B=1=1. c. Bo 4,B =1 = 1. Q4. The table below represents the relation between the type of tumor (y), where y=0 means benign and y=1 means malignant and its size in cm (x 1) and age in months (x_2). X_1 10 X_2 1 0 230 40 40 60 2 1 4 1 0 1 y Walk through the steps of finding a logistic regression model that fits the data. Define the objective function then find the updated value of the model after performing each GD iteration for a total of 3 iterations. Assuming = [1, 0.5,0], a = 0.001. Q1. The table below gives the number of hours spent studying for an ML exam (x), and the final exam grade (y). x 2 5 1 0 4 2 3 y 77 92 70 63 90 75 84 Find the linear regression model that fits the data and the predicted grade for a student who studied for 6 hours? Q2. The table below represents the relation between prices of houses (y) and their sizes (x_1) in meter square and number of rooms (x_2). X 1 40 50 50 60 100 X 2 1 2 1 2 4 y 100 110 80 120 160 a. Walk through the steps of finding a linear regression model that fits the data in a closed form expression. Define the objective function and the way you solve it to yields the final closed form solution. b. Compute the predicted price of a house of size 80m and has 3 bedrooms? c. Find the updated value of the model after performing each GD iteration for total of 3 iterations if the learning rate a = 0.001, and = [1,0.5,0]. Q3. Suppose you trained a logistic regression classifier, and your hypothesis is: fg = g(o +1x1 + Bx2) Plot the decision boundary of this classifier when: a. Bo 5. =0, = -1. b. Bo = -4,B=1=1. c. Bo 4,B =1 = 1. Q4. The table below represents the relation between the type of tumor (y), where y=0 means benign and y=1 means malignant and its size in cm (x 1) and age in months (x_2). X_1 10 X_2 1 0 230 40 40 60 2 1 4 1 0 1 y Walk through the steps of finding a logistic regression model that fits the data. Define the objective function then find the updated value of the model after performing each GD iteration for a total of 3 iterations. Assuming = [1, 0.5,0], a = 0.001.
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