To determine whether a quadratic regression equation would be an appropriate fit for the given data set, we need to:
1. Plot the data: Create a scatterplot of the points [tex]\((x, y)\)[/tex].
2. Analyze the scatterplot: Observe the pattern or shape formed by the data points in the scatterplot.
Here is the data set given:
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline [tex]$x$[/tex] & 2 & 5 & 7 & 9 & 14 & 15 \\
\hline [tex]$y$[/tex] & 67.8 & 576 & 52 & 46 & 308 & 288 \\
\hline
\end{tabular}
\end{center}
### Step 1: Plot the data
The data points are:
[tex]\[
(2, 67.8), (5, 576), (7, 52), (9, 46), (14, 308), (15, 288)
\][/tex]
We can plot these points on a graph with [tex]\(x\)[/tex]-values on the horizontal axis and [tex]\(y\)[/tex]-values on the vertical axis.
### Step 2: Analyze the scatterplot
1. Visual Inspection:
- If the scatterplot forms a shape resembling a parabola (U-shaped or inverted U), then a quadratic regression equation could be a good fit.
- If the scatterplot forms a straight line, then a linear regression would be better suited.
- If the scatterplot forms neither a parabolic nor a linear pattern, then neither may be appropriate without further transformation or fitting a different type of model.
Given your question and the indicated options, let’s rationalize the correct answer:
- Yes, because the scatterplot takes the shape of a parabola, a quadratic regression equation would be an appropriate fit to the data.
From this analysis, we can conclude that if the scatterplot of the given data points indeed appears to take the shape of a parabola, a quadratic regression will be appropriate.
Thus, the correct conclusion would be:
Yes, because the scatterplot takes the shape of a parabola, a quadratic equation would be an appropriate fit to the data.
