Kevin is trying to fit a simple linear regression model $\hat{y}=\theta_0+\theta_1 x$ on a dataset with 900 observations.
After determining $\hat{\theta_0}$ and $\hat{\theta_1}$ by minimizing mean squared error, Kevin found the following:
- For 250 inputs, his predicted value $\hat{y}$ was 1 more than the actual value $y$.
- For another 500 inputs, his predicted value $\hat{y}$ was 0.5 less than the actual value $y$.
- All other points were predicted perfectly.
Calculate the mean squared error of Kevin's model. Select the closest answer. (Note that this question is not asking about mean nearest squared error.)
- 0
- 0.25
- 0.35
- 0.42
