numpy as np import numpy.polynomial.polynomial as poly

Given points

x_points = np.array([1, 3, 4, 5]) y_points = np.array([4, 7, 6, 1])

Perform quadratic regression (second-degree polynomial fit)

coefficients = np.polyfit(x_points, y_points, 2)

Coefficients are in descending powers of x, i.e., [a, b, c] for y(x) = ax^2 + bx + c

coefficients = np.round(coefficients, 4)

coefficientsThe quadratic regression curve for the given points is:

$y(x) = -1.2045x^2 + 6.5409x - 1.4000$

Would you like further details or any clarifications?

Here are 5 related questions for deeper understanding:

1. How do we interpret the coefficients of the quadratic regression?
2. What is the significance of quadratic regression in data analysis?
3. How would you calculate the residuals for this regression model?
4. What would be the effect of adding more data points to the regression curve?
5. How can you use this quadratic model for prediction?

Tip: To better understand regression, graphing the data points and the regression curve can give you a visual sense of how well the curve fits the data.