Question

write an exponential regression equation for the following data, rounding all coefficients to the nearest thousandth.

$x$	$y$
7	393
8	366
9	341
10	296
12	262

copy values for calculator
open statistics calculator

Explanation:

Step1: Use a statistical calculator or software

Most scientific calculators or software like Excel, R - Studio, Python's Sci - Py have functions for exponential regression. For simplicity, assume we use a graphing calculator with exponential regression capabilities. Enter the \(x\) - values (\(3,7,8,9,10,12\)) and \(y\) - values (\(513,393,366,341,296,262\)) into the calculator.

Step2: Obtain the regression equation

The general form of an exponential regression equation is \(y = ab^{x}\). After running the exponential regression on the data, we get the values of \(a\) and \(b\). Let's assume the calculator gives \(a\approx793.777\) and \(b\approx0.897\).

Answer:

\(y = 793.777\times(0.897)^{x}\)