The ability to jump helps salamanders move quickly to avoid predators. A paper investigated jumping
behavior of 10 species of salamanders and reported the following data on bend angle (the bend [in
degrees] in the salamander body, with a larger number reflecting more extreme bending) and the jump
takeoff velocity (in meters per second). There is a positive correlation between bend angle and takeoff
velocity.
Bend Angle Takeoff Velocity
36.4 0.6
54.9 0.7
43.4 0.7
50.3 0.7
69.9 0.9
71.3 1.0
67.5 1.1
48.0 0.7
61.9 0.9
52.5 0.9
(a) If the goal is to learn about how takeoff velocity is related to salamander bend angle, which of these
two variables is the response variable and which is the predictor variable?
The predictor variable (x) is takeoff velocity and the response variable (y) is bend angle.
The predictor variable (x) is bend angle and the response variable (y) is takeoff velocity
(b) Construct a scatterplot of these data. Would it be reasonable to use a line to summarize the
relationship between takeoff velocity and bend angle?
It would not be reasonable to use a line to summarize the relationship between takeoff
velocity and bend angle.
It would be reasonable to use a line to summarize the relationship between takeoff velocity
and bend angle.
(c) Find the equation of the least squares regression line. (Round your numerical values to four decimal
places.)
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Using statistical software to calculate the least squares regression line, we can obtain the equation of the line:
Bend Angle = -17.3582 + 0.0323 * Takeoff Velocity