Question

determine the quadratic regression equation for the following data.

x	1	2	3	4	5	6	7	8	9	10
y	73	26	22	5	6	13	13	36	57	96

○ y = 3.75758x² - 38.1515x + 99.8667
○ y = 2.46831x² + 11.9219x + 118.0781
○ y = 2.71412x² - 47.5133x + 107.4289
○ y = 3.17439x² + 27.1918x + 112.5589

Explanation:

Step1: Use a statistical software or calculator

Most scientific - calculators or software like Excel, R, Python (with libraries like numpy and scipy.stats) have functions to perform quadratic regression. For simplicity, assume we use a statistical software or calculator with quadratic regression functionality. We input the \(x\) - values \(\{1,2,\cdots,10\}\) and the corresponding \(y\) - values \(\{73,26,22,5,6,13,13,36,57,96\}\) into the software.

Step2: Obtain the regression equation

The software will calculate the coefficients \(a\), \(b\), and \(c\) for the quadratic regression equation \(y = ax^{2}+bx + c\).

Answer:

By using a statistical software or calculator for quadratic regression on the given data, we find that the quadratic regression equation is \(y = 3.75758x^{2}-38.1515x + 99.8667\). So the answer is \(y = 3.75758x^{2}-38.1515x + 99.8667\).