Omer trained a linear regression model and tested its...

Omer trained a linear regression model and tested its performance on a test sample of 500 objects. On 400 of those, the model returned a prediction higher than expected by 0.5, and on the remaining 100, the model returned a prediction lower than expected by 0.7. What is the MSE for his model? Limor claims that the linear regression model wasn't trained correctly, and we can do improve it by changing all the answers by a constant value. What will be her MSE? You can assume that Limor found the smallest error under her constraints. Return two values - Omer's and Limor's MSE.

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00:01 So for this problem, we have that the mean squared error is going to be equal to the square root of the sum, the difference between each observation and the predicted observation squared.

00:20 Oh, actually, that would be rmse.

00:22 Pardon me, we're not taking the square root.

00:24 Ignore that part.

00:25 So we take the square of the error of the prediction and the actual value for each data point.

00:32 Then we divide that by the number of observations, which we're told is 500.

00:38 Now, we know that on 400 of the observations, the model predicted or returned a prediction that was higher by 0 .5.

00:50 So we'd have four times negative 0 .5 to the power of 2 because the error, if the prediction is higher, the error would be a negative value.

00:59 And then we'd have plus 100 times, we're told the model predicted a, or the prediction was lower than expected by 0 .7.

01:11 So we'd have plus 100 times 0 .7 to the power of 2.

01:16 And then we divide that value by 500 to get the mean squared error.

01:20 So 400 times 0 .5 to the power of 2 would be 0 .25, plus 100 times 0 .7.

01:30 The power of 2.

01:33 In the numerator, we get 149.

01:38 In the denominator, well, we still have 500.

01:41 So when we divide 149 by 500, we get a result that the mean squared error is equal to 0 .298...

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