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Unit 1: Introduction

20252m

The training dataset has 5 samples with predicted outputs [2,3,5,4,6] and actual outputs [3,3,4,5,6]. What is the Mean Squared Error (MSE)?
(i) 0.2
(ii) 0.4
(iii) 0.5
(iv) 0.6

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Answer: (iv) 0.6

Calculation:

Mean Squared Error: MSE=1n∑i=1n(yi−y^i)2MSE = \frac{1}{n}\sum_{i=1}^n (y_i - \hat{y}_i)^2

Given:
Predicted y^=[2,3,5,4,6]\hat{y} = [2,3,5,4,6], Actual y=[3,3,4,5,6]y = [3,3,4,5,6], n=5n=5

i yiy_i y^i\hat{y}_i yi−y^iy_i-\hat{y}_i (yi−y^i)2(y_i-\hat{y}_i)^2
1 3 2 1 1
2 3 3 0 0
3 4 5 -1 1
4 5 4 1 1
5 6 6 0 0
Sum squared error =1+0+1+1+0=3=1+0+1+1+0=3

MSE=3/5=0.6MSE = 3/5 = 0.6

Hence (iv) 0.6 is correct. (0.2 would be MAE, not MSE).

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