To determine the exponential regression equation that fits the given data points:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 4 \\
\hline
2 & 8 \\
\hline
3 & 27 \\
\hline
4 & 85 \\
\hline
5 & 250 \\
\hline
6 & 600 \\
\hline
\end{array}
\][/tex]
we need to find an equation of the form [tex]\( y = a \cdot b^x \)[/tex].
Using the parameters [tex]\( a = 2.233965481826066 \)[/tex] and [tex]\( b = 2.542177114552428 \)[/tex], the regression equation is:
[tex]\[
y = 2.233965481826066 \cdot (2.542177114552428)^x
\][/tex]
We need to compare this with the given options:
A. [tex]\( y = 2.84 \left(1.22^x\right) \)[/tex]
B. [tex]\( y = 1.22 \left(2.84^x\right) \)[/tex]
C. [tex]\( y = 41.32 x^2 - 181.7 x + 171.6 \)[/tex]
D. [tex]\( y = 107.54 x - 214.06 \)[/tex]
None of the provided options exactly match our regression equation. Therefore, based on our calculated parameters, none of the choices provided correctly represent the exponential regression equation that fits the given data.
To summarize:
- The correct exponential regression equation is [tex]\( y = 2.233965481826066 \cdot (2.542177114552428)^x \)[/tex].
- None of the given choices (A, B, C, or D) match this equation.
