Question

1,2,3,4,5

6% Edit PDF View Annotate Go Window Help Annatate TI Edit 0% v - + Try Full Version Lab Activity- Linear Modeling- BMX(1) TO A A What's Weight 6ot to Do wth H? Name 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. 9.8 9.79 9.7 9.6 Height (inches) Weight (pounds) 10.35 10.3 10.25 10.2 10.1 9.85 22.5 23 23.5 24 19 19.5 20 20.5 21 22 1. Consider which quantity should be represented by the dependent variable, typically y, and which quantity should be represented by the independent variable, typically x. Ask yourself, "Does the height of the jump depend on the weight of the bike? Or does the weight of the bike depend on the height of the jump?" One of the quantities "depends" on the other. Instead of using the letters "y and "x, feel free to choose letters that more readily identify what those letters represent, for example "h" for height and "w for weight. List your choices then plot the data using DESMOS. Here is a video that can help! Variable chosen to represent this quantity Independent quantity Variable chosen to represent this quantity Dependent quantity Does the data appear to be linearly related? 2. Find a linear equation that models the data. Use the linear regression tool in DESMOS. Round the values you calculate for the slope and the y-intercept to the nearest hundredth. Linear model: AS 4,093 НИИИ iew Annotate Edit PDF Go Window Help TI Edit Annotate Try Full Version Lab Activity Linear Modeling BMX(1) A A TO rwurn une values you calculate for the slope and the y-intercept to the nearest hundredth. Linear model: 3. Write a sentence that interprets the slope of the linear model.. Use numerical quantities and contextual descriptors in your explanation. 4. 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? Need a video on correlation? Correlation coefficient: Characterization: 5. Using your linear model, predict the maximum height of a jump for a bike weighing 25 pounds. Show your work and round your answer to the nearest hundredth of an inch. 4083 Maciod

Answer 1

Answer

1.

In the question, it is mentioned that the height of the jump depends on the weight of the bike.

Hence,

Independent quantity - Weight(pounds) Variable that represents this quantity - w

Dependent quantity - Height(inches) Variable that represents this quantity - h

Does the data appear to be linearly related? Yes

Below is the plot of the data using the tool.

h 20 10 15 20 25 -20- LO LE

2.

h 20 10 15 20 25 -20- LO LE

Using the regression tool, the linear equation that models the data is

h 0.16w13.35

The slope value is -0.16.

The y-intercept value is 13.35.

9.85 22 22.5 9.8 9.79 23 9.7 23.5 24 9.6 h mwb RESIDUALS STATISTICS 2=0.9824 e plot r0.9912 PARAMETERS b 13.348 m=-0.156 st

3.

Interpretation of the slope

If the weight of the bike increases by 1 pound, then the model predicts that the height of maximum jump decreases by approximately 0.16 inch.

The model predicts that the height of maximum jump decreases as weight increases.

4.

The correlation coefficient of the model is

=0.99

The correlation is strong.

5.

The maximum jump height of a bike weighing 25 pounds is

h 0.16(25) 13.35 413.35 9.35 inches