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CMSC471 Intro to Artificial Intelligence

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CMSC471 Intro to Artificial Intelligence
16. (12 points) Equation 2 shows how MSE is calculated in Linear Regression, and Equation 3
shows how MAE is calculated where m is number of samples. Equation 4 shows how each
predicted value ˆy(i) is calculated.
MSE(θ) = 1
m
�m
i=1
(θT x(i) − y(i)
)2 (2)
MAE(θ) = 1
m
�m
i=1
| θT x(i) − y(i) | (3)
yˆ(i) = θ0 + θ1×1 + θ2×2 + θ3×3 + θ4×4 (4)
A regression model has been trained on a separate training set and the trained model parameters
(θ) vector is as follows:
θ = {θ0 = 0, θ1 = 2, θ2 = 1, θ3 = 0.5, θ4 = −1}
The regression test dataset for four samples is given in Figure 3. Each sample has values for
the four features {x1, x2, x3, x4} as well as the actual target value y(i)
Figure 3: Regression Dataset
(part a – 6 points) Compute MSE – show your complete work. (Hint: Compute the predicted
value ˆy(i) for each sample and then put them in Equation 2)
(part b – 6 points) Compute MAE – show your complete work. (Hint: Compute the predicted
value ˆy(i) for each sample and then put them in Equation 3)
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