Use the provided dataset to construct the Cubic spline.

Plot the original data points and the cubic spline interpolated curve on

the same graph.

$3$: Newton's Divided Difference

i$.$ Newton's Divided Difference:

Implement the Newton's divided difference method for polynomial

interpolation.

Use the provided dataset to construct the Newton's interpolating

polynomial.

Plot the original data points and the interpolated curve.

Calculate and display the divided difference table. $1$: Linear and Polynomial Regression:

i$.$ Linear Regression:

Load the provided dataset containing data points, example of MATLAB

code

data $=$ load$(\text{'}$data$.$txt$\text{'})$;

$y=$data$($:$,2)$;

Implement the linear regression formula.

Fit a linear regression model to the data.

Plot the original data points and the fitted line on the same graph.

Calculate and display the coefficients of the linear model.

ii$.$ Polynomial Regression:

Implement the polynomial regression formula.

Fit polynomial regression models of degree $2$ and $3$ to the same dataset.

Plot the original data points and the fitted polynomial curves on the

same graph for each degree.

Calculate and display the coefficients of the polynomial models.

$2$: Lagrange Interpolation and Cubic Spline

i$.$ Lagrange Interpolation:

Implement the Lagrange interpolation formula.

Use the provided dataset to construct the Lagrange interpolating

polynomial.

Plot the original data points and the interpolated curve.

ii$.$ Cubic Spline Interpolation:

Implement the Cubic spline formula.