2. You have been hired by the European Space Agency to build a model that predicts the amount of oxygen that an astronaut consumes when performing five minutes of intense physical work. The descriptive features for the model will be the age of the astronaut and their average heart rate throughout the work. The regression model is OXYCON = w[0] + w[1] × AGE + w[2] × HEARTRATE The table below shows a historical dataset that has been collected for this task.

a. Assuming that the current weights in a multivariate linear regression model are w[0] = −59.50, w[1] = −0.15, and w[2] = 0.60, make a prediction for each training instance using this model.

b. Calculate the sum of squared errors for the set of predictions generated in part (a).

c. Assuming a learning rate of 0.000002, calculate the weights at the next iteration of the gradient descent algorithm.

d. Calculate the sum of squared errors for a set of predictions generated using the new set of weights calculated in part (c).

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ID OXYCON AGE HEART RATE 1 37.99 41 138 2 47.34 42 153 3 44.38 37 151 4 28.17 46 133 5 27.07 48 126 6 37.85 44 145 7 44.72 43 158 8 36.42 46 143 9 31.21 37 138 10 54.85 38 158 11 39.84 43 12 30.83 ** 143 43 138