Lab 3-Nadaraya–Watson kernel regression

The lab have 3 part:

Part 1 Simulation:
This lab started by Implementing by hand a Kernel Regression a non-parametric regression.
Also, Implement by hand 5 cross-validation.
Compute different Error Measures:
1.EOP= Expected optimism of regression function.

$$EOP=\frac{2\sigma^{2}}{n}Tr(W)\ \ \ ,W\in\mathbb{R}^{n\times n} \ \ weight\ matrix$$.

2.EPEIN= In-sample expected error of regression function
$$\hat{EPE_{in}}=\overline{\epsilon}+\hat{EOP}$$ 3.EPE=out-of-sample expected prediction error of regression function.
$$E[EPE-EPE_{in}]$$

Part 2 estimates the rate of change in Covid-19
Extract estimate the rate of change in Covid-19 (Coronavirus) case data in Israel.
The data can be found at https://github.com/idandrd/israel-covid19-data/blob/master/IsraelCOVID19.csv.
by using the first derivative of the regression curve.

Part 3 fit prediction models for the response voxels
Finally fit prediction models for the response voxels (Y) in V1 in response to natural images (X).