Description
Question 1 (Linear regression)
The following is a table of data to be used for linear regression. This table describes the expenditure (in
dollars) on recreation per month by employees at a certain company, and their corresponding monthly
incomes. We treat the left-hand column as the input and the right-hand column as the output. Considering the
bias parameter in your computation.
Answer the following questions:
a. Find the equation of the linear regression line for the data
b. What is the slope? What is the y-intercept?
c. Using the equation for the linear regression that you calculated, estimate the monthly income of an
employee at this company who spends 5000 dollars per month on recreation.
Question 2 (Binary perceptron)
Apply the binary perceptron algorithm for the following data set. The training samples (i.e., 3D data points
with the corresponding labels) are given as the following table.
# Features (x1, x2, x3) Class label
1 (4,3,6) –
2 (2,-2,3) +
3 (1,0,-3) +
4 (4,2,3) –
Start with weight vector π€ = (π€0, π€1, π€2,π€3) = (1,0,0,0), where π€0 is the bias parameter. Then, you need to use
the bias feature together with given features during your computation.
a. Will the perceptron algorithm converge? Write βnever” if it will never converge and prove.
b. If the perceptron algorithm converges, fill out the table below. After how many steps will the perceptron
algorithm converge? Note: one step means processing one data point. Data points are processed in order
and then repeated, until convergence.
Step Weights Score Correct?
1 (1,0,0,0)
Final weights:
Question 3 (Multi-class perceptron)
Consider a multi-class perceptron with current weight vectors wA = (1, 2, 3), wB = (-1, 0, 2), wC = (0, -2, 1).
A new training sample is provided, which has feature vector x = (x0, x1, x2) = (1, -3, 1) and label y* = B. Here,
x0 is the bias feature.
a. Which class y would be predicted by the current weight vectors?
b. Would the perceptron update the weight vectors after having seen this training example? If yes, write the
resulting weight vectors below:
wA =
wB =
wC =
