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What is the quadratic regression equation that fits these data?

[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 35 \\
\hline
-3 & 20 \\
\hline
-2 & 12 \\
\hline
-1 & 6 \\
\hline
0 & 2 \\
\hline
1 & 6 \\
\hline
2 & 10 \\
\hline
3 & 24 \\
\hline
4 & 38 \\
\hline
\end{array}
\][/tex]

A. [tex]\(y = 2.09x^2 + 0.33x + 3.06\)[/tex]
B. [tex]\(y = 0.84x^2 + 0.22x + 4.38\)[/tex]
C. [tex]\(y = 2.84x^2 + 0.68x + 1.12\)[/tex]
D. [tex]\(y = 12.09 \cdot 1.01^x\)[/tex]

Sagot :

GinnyAnswer
To determine which quadratic regression equation best fits the given data points, we need to perform a quadratic regression analysis. The general form of a quadratic equation is:

[tex]\[ y = ax^2 + bx + c \][/tex]

We're looking for the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] that will result in the equation that best fits the provided data points:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -4 & 35 \\ \hline -3 & 20 \\ \hline -2 & 12 \\ \hline -1 & 6 \\ \hline 0 & 2 \\ \hline 1 & 6 \\ \hline 2 & 10 \\ \hline 3 & 24 \\ \hline 4 & 38 \\ \hline \end{array} \][/tex]

After performing the quadratic regression analysis on these data points, the coefficients found were:
[tex]\[ a = 2.09 \][/tex]
[tex]\[ b = 0.33 \][/tex]
[tex]\[ c = 3.06 \][/tex]

Thus, the quadratic regression equation that fits the data is:

[tex]\[ y = 2.09x^2 + 0.33x + 3.06 \][/tex]

Checking the provided options, the correct answer is:

A. [tex]\( y = 2.09x^2 + 0.33x + 3.06 \)[/tex]
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