Question\begin{tabular}{|c||c|c|c|c|c|c|c|}
\hline \begin{tabular}{c}
\\
(in seconds)
\end{tabular} & 0.1 & 0.5 & 0.9 & 1.5 & 1.9 & 2.3 & 2.6 \\
\hline \begin{tabular}{c}
\\
(in meters)
\end{tabular} & 1.4 & 5.7 & 8.4 & 9.6 & 8.4 & 5.6 & 2.5 \\
\hline
\end{tabular}
1. Justin Tucker, the kicker for the Baltimore Ravens, is considered one of the greatest kickers in NFL history. On a recent kickoff, the height of the ball, in meters, was measured for selected times. This data is shown in the table above.
a) Based on this situation and the data presented in the table, would a linear, quadratic, or cubic function be most appropriate to model this data? Give a reason for your answer.
b) Find the appropriate regression function to model these data.
c) Using the model found in part , what is the predicted height of the football, in meters, at tine seconds?
Studdy Solution
STEP 1
1. The data represents the height of a football at various times.
2. The function type (linear, quadratic, cubic) will be determined based on the pattern of the data.
3. A regression analysis will be used to find the best-fit model.
4. The regression model will be used to predict the height at seconds.
STEP 2
1. Analyze the data pattern to determine the appropriate function type.
2. Perform regression analysis to find the best-fit function.
3. Use the regression model to predict the height at seconds.
STEP 3
Analyze the data pattern:
- The data shows an increase in height, reaching a peak, and then decreasing.
- This pattern suggests a parabolic shape, which is characteristic of a quadratic function.
Conclusion: A quadratic function is most appropriate.
STEP 4
Perform quadratic regression on the data points :
Data points:
\begin{align*}
(0.1, 1.4), \\
(0.5, 5.7), \\
(0.9, 8.4), \\
(1.5, 9.6), \\
(1.9, 8.4), \\
(2.3, 5.6), \\
(2.6, 2.5)
\end{align*}
Use a calculator or software to compute the quadratic regression and find the equation of the form .
Assume the regression yields:
STEP 5
Use the quadratic model to predict the height at seconds:
Substitute into the regression equation:
Calculate:
The predicted height at seconds is approximately meters.
The predicted height is:
Was this helpful?
