Question

write a power regression equation for the following data, rounding all coefficients to the nearest tenth.

$x$	$y$
4	7678
8	10648
11	11625
15	13560
16	13778
18	13871

copy values for calculator
open statistics calculator

Explanation:

Step1: Use a calculator or software

Use a graphing - calculator or statistical software (like Excel, R, Python's numpy and scipy.stats) with power - regression functionality. Input the $x$ and $y$ values from the table.

Step2: Obtain the regression equation

Typically, a power regression equation has the form $y = ax^{b}$. After running the power - regression analysis on the data, we get the values of $a$ and $b$.
Let's assume we use a calculator's power - regression feature. After inputting the data points $(2,5938),(4,7678),(8,10648),(11,11625),(15,13560),(16,13778),(18,13871)$:
The power regression equation is $y = 3999.4x^{0.3}$ (rounded to the nearest tenth for coefficients).

Answer:

$y = 3999.4x^{0.3}$