Question

Q1: Linear model for regression X Y 2 15 3 20 4 40 Consider a linear-regression model with n = 1 and m = 3 with (X, Y) pairs as shown in the table above, what is $\frac{\partial E(W)}{\partial w_1}$ (the gradient of MSE with respect to $w_1$), when $w_0 = 0$ and $w_1 = 1$? Q2: Linear model for classification (perceptron) A. What is the value of $w_0$, $w_1$, $w_2$ if you perform the perceptron algorithm on the following training set when the initial weight of w = {0,1,1}, Iterations=2, activation function = sign, threshold =0, a=1 $X_1$ $X_2$ Y 1 1 1 0 1 -1 B. Draw the decision boundary using the estimated weight. Q3: Linear Model for classification (logistic regression) 1. Suppose you have trained a logistic regression classifier for cancer prediction (cancer is the positive class) given the cell size ($x_1$), and the best estimated parameters are $w_0 = 0.2$, $w_1 =$ 0.1. What is the probability that a patient cell is cancerous if the cell size ($x_1$) = 3.5 centimeters?

          Q1: Linear model for regression
X
Y
2
15
3
20
4
40
Consider a linear-regression model with n = 1 and m = 3 with (X, Y) pairs as shown in the table
above, what is $\frac{\partial E(W)}{\partial w_1}$ (the gradient of MSE with respect to $w_1$), when $w_0 = 0$ and $w_1 = 1$?
Q2: Linear model for classification (perceptron)
A. What is the value of $w_0$, $w_1$, $w_2$ if you perform the perceptron algorithm on the following
training set when the initial weight of w = {0,1,1}, Iterations=2, activation function =
sign, threshold =0, a=1
$X_1$
$X_2$
Y
1
1
1
0
1
-1
B. Draw the decision boundary using the estimated weight.
Q3: Linear Model for classification (logistic regression)
1. Suppose you have trained a logistic regression classifier for cancer prediction (cancer is the
positive class) given the cell size ($x_1$), and the best estimated parameters are $w_0 = 0.2$, $w_1 =$
0.1. What is the probability that a patient cell is cancerous if the cell size ($x_1$) = 3.5
centimeters?

Q1: Linear model for regression
X
Y
2
15
3
20
4
40
Consider a linear-regression model with n = 1 and m = 3 with (X, Y) pairs as shown in the table
above, what is (∂ E(W))/(∂ w1) (the gradient of MSE with respect to w1), when w0 = 0 and w1 = 1?
Q2: Linear model for classification (perceptron)
A. What is the value of w0, w1, w2 if you perform the perceptron algorithm on the following
training set when the initial weight of w = 0,1,1, Iterations=2, activation function =
sign, threshold =0, a=1
X1
X2
Y
1
1
1
0
1
-1
B. Draw the decision boundary using the estimated weight.
Q3: Linear Model for classification (logistic regression)
1. Suppose you have trained a logistic regression classifier for cancer prediction (cancer is the
positive class) given the cell size (x1), and the best estimated parameters are w0 = 0.2, w1 =
0.1. What is the probability that a patient cell is cancerous if the cell size (x1) = 3.5
centimeters?

Added by Michelle B.

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