In BMX dirt bike racing, jumping high (or “getting air”) depends on many factors including rider’s skill, angle of the jump, and weight of the bike. Here is data about the maximum jump heights for various bike weights. Height (inches) 10.35 10.3 10.25 10.2 10.1 9.85 9.8 9.79 9.7 9.6 Weight (pounds) 19 19.5 20 20.5 21 22 22.5 23 23.5 24 1. Sketch a graph of the data. Consider which quantity should be the dependent variable and which quantity should be the independent variable. Does the data appear to be linearly related? 2. Examine the graph of the data using a graphing utility. Find an equation that models the data. Use a linear regression calculation tool. Round your answers to the nearest hundredth. 3. Write a sentence to interpret the slope of the equation that models the data. Use numerical quantities and contextual descriptors. 4. Write a sentence explaining the meaning, in context, of the y-intercept of the model. 5. What is the correlation coefficient for your model? Round your answer to the nearest hundredth. Would you characterize the correlation as weak, medium, or strong? 6. Using your model, predict the maximum height of a jump for a bike weighing 25 pounds. Round your answer to the nearest hundredth of an inch.
In BMX dirt bike racing, jumping high (or “getting air”) depends on many factors including rider’s skill,
angle of the jump, and weight of the bike. Here is data about the maximum jump heights for various bike
weights.
Height
(inches)
10.35 10.3 10.25 10.2 10.1 9.85 9.8 9.79 9.7 9.6
Weight
(pounds)
19 19.5 20 20.5 21 22 22.5 23 23.5 24
1. Sketch a graph of the data. Consider which quantity should be the dependent variable and which
quantity should be the independent variable. Does the data appear to be linearly related?
2. Examine the graph of the data using a graphing utility. Find an equation that models the data. Use a
linear regression calculation tool. Round your answers to the nearest hundredth.
3. Write a sentence to interpret the slope of the equation that models the data. Use numerical quantities
and contextual descriptors.
4. Write a sentence explaining the meaning, in context, of the y-intercept of the model.
5. What is the
Would you characterize the correlation as weak, medium, or strong?
6. Using your model, predict the maximum height of a jump for a bike weighing 25 pounds. Round your
answer to the nearest hundredth of an inch.
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