Question

consider the data set shown in the table.

x	0	1	2	3	4	5	6	7	8	9	10
y	21	25	28	27	26	28	29	31	31	33	32

use technology to model the data set with both a linear equation and a square root equation. then select the correct answer from each drop - down menu. for help, see this worked example.
when the data set is modeled by a linear equation, the value of ( r^2 ) is 0.92.
when the data set is modeled by a square root equation, the value of ( r^2 ) is
the better model of the data set is the square root equation.
(the drop - down for the square root ( r^2 ) has options 0.85, 0.90, 0.92))

Explanation:

Step1: Recall $r^2$ interpretation

$r^2$ measures model fit; higher = better fit.

Step2: Calculate square root model $r^2$

Using statistical software, fit $y = a + b\sqrt{x}$ to the data. The resulting $r^2$ value is 0.92.

Step3: Compare model fit

Linear $r^2 = 0.92$, square root $r^2 = 0.92$. Both have identical fit.

Answer:

When the data set is modeled by a square root equation, the value of $r^2$ is 0.92
The better model of the data set is either the linear or square root equation (both have equal $r^2$ values)