To determine whether a quadratic regression equation is appropriate for the given data set, let's follow these steps:
1. Plot the Data Points on a Scatterplot:
- To plot the data points, you create a graph where the x-values are on the horizontal axis and the y-values are on the vertical axis.
- The data points are given as:
- (2, 56)
- (5, 14)
- (7, 119)
- (9, 119)
- (14, 42)
- (15, 133)
2. Examine the Pattern of the Data Points:
- Plot each of these points on the scatterplot.
- After plotting, look at the pattern formed by the points.
It's important to note that the shape of the data points will dictate the type of regression that fits best. Since quadratic regression fits parabolic curves (which have a "U" shape, either opening up or down), you need to see if the pattern suggests this type of curve.
From your description:
- You mentioned that the scatterplot takes the shape of a parabola.
Thinking about the characteristics of the data points:
- (2, 56)
- (5, 14)
- (7, 119)
- (9, 119)
- (14, 42)
- (15, 133)
Analyzing these points visually, observe the overall pattern:
- They don't strictly line up.
- They show peaks and troughs which would suggest the potential of a parabolic shape.
3. Conclusion:
Given that the scatterplot suggests a parabolic shape and considering that quadratic regression fits a parabolic pattern, we can conclude that a quadratic regression equation would be appropriate.
So, the correct statement is:
- Yes.
A quadratic regression equation is suitable when the data suggests a parabolic trend, which seems to be the case after visual inspection of your scatterplot.
