Step 1 :Given the data points, we want to find the best fit quartic function. A quartic function is of the form \(y = ax^4 + bx^3 + cx^2 + dx + e\).
Step 2 :We use the method of least squares to find the coefficients \(a\), \(b\), \(c\), \(d\), and \(e\). This involves setting up a system of equations based on the sum of the squares of the residuals (the differences between the observed and predicted values), and then solving this system.
Step 3 :By solving the system of equations, we find the coefficients of the quartic function to be approximately -0.250, 0, -1.000, 0, and 0. These coefficients correspond to the terms \(x^4\), \(x^3\), \(x^2\), \(x\), and the constant term, respectively.
Step 4 :Therefore, the best fit quartic function for the given data is \(y = -0.250x^4 - 1.000x^2\).