Question

A punter for a football team is trying to determine the optimal angle for striking the football off his foot—this is called the launch angle. Using video, his coach records a number of punts kicked using different launch angles and the height in feet for each punt. A regression equation for this relationship is Height hat = 2.31 (angle) minus 39.389. A graph titled Residuals versus Launch angle has launch angle (Degrees) on the x-axis, and residual on the y-axis. Points decrease, and then curve up. Based on the residual plot shown, is a linear model appropriate for using launch angle to predict height? A linear model is appropriate because the residual plot is curved. A linear model is appropriate because many of the residuals are close to zero. A linear model is not appropriate because the residual plot shows a clear pattern. A linear model is not appropria

Answer 1

A linear model is not appropriate for predicting the height of a kicked football based on launch angle, as the residual plot exhibits a clear pattern, suggesting a non-linear relationship.

Step-by-step explanation:

The question is concerning the appropriateness of a linear model for predicting the height of a football when kicked at different launch angles. Based on the given information where a residual plot shows a curved pattern, we can infer that a linear model is not appropriate because the residuals do not scatter randomly around zero but instead show a clear pattern indicating that the relationship between launch angle and height is not linear. As the residuals decrease and then curve upwards, this suggests that a different type of model, perhaps quadratic or some other non-linear model, might be better suited for this data set.