Machine Learning Foundations, End Term

September 2025 term, 21 Dec 2025, Set 2

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Question 1

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A real estate company wants to create a model to predict house prices based on the size of the house. They collect data from three recent sales. There are two features: size (hundreds of sq ft) and number of bedrooms. The data-matrix and the price vector (in hundreds of thousands of rupees) are:

The objective is to find the weight vector that minimizes the sum of squared errors given by the loss function:

If is the value that minimizes , then which of the following is ?

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A real estate company wants to create a model to predict house prices based on the size of the house. They collect data from three recent sales. There are two features: size (hundreds of sq ft) and number of bedrooms. The data-matrix and the price vector (in hundreds of thousands of rupees) are: The objective is to find the weight vector that minimizes the sum of squared errors given by the loss function: If is the value that minimizes , then which of the following is ? A real estate company wants to create a model to predict house prices based on the size of the house. They collect data A real estate company wants to create a model to predict house prices based on the size of the house. They collect data Let . Find the directional derivative of at the point in the direction of unit vector along . Consider the convex hull of the set of points . Which of the following points belongs to the convex hull?