Determine the quadratic regression for the data. {(1, 5), (3, 4), (4, 1), (5, 2), (7, 4)} Explain how you got your answers. Round to the nearest hundredth.

Answer 1

To determine the quadratic regression for the given data set, we will first write out the quadratic equation in the form of y = ax^2 + bx + c. We can then use the given points to create a system of equations and solve for the coefficients a, b, and c.

Using the given data points:
(1, 5), (3, 4), (4, 1), (5, 2), (7, 4)

We get the system of equations:
a + b + c = 5 (1)
9a + 3b + c = 4 (2)
16a + 4b + c = 1 (3)
25a + 5b + c = 2 (4)
49a + 7b + c = 4 (5)

Using matrices or substitution method to solve the system of equations, we get:
a = -0.16, b = 3.69, c = 1.47

Therefore, the quadratic regression for the data set is y = -0.16x^2 + 3.69x + 1.47.