MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
![### Quadratic Regression Analysis of an Object in Free Fall
#### Given Data:
The table below shows the height, \( h \), in meters, of an object that is thrown off the top of a building as a function of \( t \), the time in seconds after it is thrown.
| \( t \) (seconds) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
|-------------------|--------|------|------|------|--------|-------|
| \( h(t) \) (meters) | 69.325 | 82.2 | 92.625 | 100.6 | 106.125 | 109.2 |
#### Instructions:
Using your calculator to do a quadratic regression, express the height of the object as a function of the number of seconds that have passed since the object was thrown.
***Round all numbers to 1 decimal place.***
#### Problem-Solving:
1. **Using your quadratic regression, how high will the object be 2.8 seconds after it is thrown?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
2. **Using your quadratic regression, how long will it take the object to reach 24 meters?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
### Explanation of Concepts:
- **Quadratic Regression:** This is a process of finding the equation of the parabola that best fits a set of data points. It is generally used in scenarios where the relationship between a dependent variable \( y \) and an independent variable \( x \) is parabolic.
### Graphs and Diagrams:
In this task, you will use a quadratic regression calculator tool to find the quadratic equation in the form:
\[ h(t) = at^2 + bt + c \]
Where:
- \( h(t) \) is the height in meters.
- \( t \) is the time in seconds.
- \( a \), \( b \), and \( c \) are coefficients determined through regression analysis.
Once you have the equation, you can substitute \( t = 2.8 \) to find the height at 2.8 seconds and solve for \( t \) when \( h(t)](https://content.bartleby.com/qna-images/question/badf131f-ca26-4f8e-953f-35e945c24016/11c8e8b3-944f-4c09-81f4-7efcef2c7dab/u3a1kvd_processed.jpeg)
Transcribed Image Text:### Quadratic Regression Analysis of an Object in Free Fall
#### Given Data:
The table below shows the height, \( h \), in meters, of an object that is thrown off the top of a building as a function of \( t \), the time in seconds after it is thrown.
| \( t \) (seconds) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
|-------------------|--------|------|------|------|--------|-------|
| \( h(t) \) (meters) | 69.325 | 82.2 | 92.625 | 100.6 | 106.125 | 109.2 |
#### Instructions:
Using your calculator to do a quadratic regression, express the height of the object as a function of the number of seconds that have passed since the object was thrown.
***Round all numbers to 1 decimal place.***
#### Problem-Solving:
1. **Using your quadratic regression, how high will the object be 2.8 seconds after it is thrown?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
2. **Using your quadratic regression, how long will it take the object to reach 24 meters?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
### Explanation of Concepts:
- **Quadratic Regression:** This is a process of finding the equation of the parabola that best fits a set of data points. It is generally used in scenarios where the relationship between a dependent variable \( y \) and an independent variable \( x \) is parabolic.
### Graphs and Diagrams:
In this task, you will use a quadratic regression calculator tool to find the quadratic equation in the form:
\[ h(t) = at^2 + bt + c \]
Where:
- \( h(t) \) is the height in meters.
- \( t \) is the time in seconds.
- \( a \), \( b \), and \( c \) are coefficients determined through regression analysis.
Once you have the equation, you can substitute \( t = 2.8 \) to find the height at 2.8 seconds and solve for \( t \) when \( h(t)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps
Knowledge Booster
Similar questions
- A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-0.799 b=23.923 p²=0.695556 r=-0.834 Use this to predict the number of situps a person who watches 1 hours of TV can do (to one decimal place)arrow_forwardA regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=a+bx b=-0.66 a=25.376 r²=0.390625 r=-0.625 Use this to predict the number of situps a person who watches 2.5 hours of TV can do. place. Round to one decimalarrow_forwardA regression was run to determine if there is a relationship between hours of study per week (x) and the final exam Scores (y). The results of the regression were: y=ax+b a=6.179 b=28.96 r²=0.937024 r=0.968 Use this to predict the final exam score of a student who studies 4 hours per week, and please round your answer to a whole number.arrow_forward
- A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were :ŷ=a+bx a=20.874 b=-0.638 r2=0.894916 r=-0.946 Use this to predict the number of situps a person who watches 8 hours of TV can do (to one decimal place) _________arrow_forwardA regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-0.971 b=21.794 r²-0.872356 r=-0.934 Use this to predict the number of situps a person who watches 5 hours of TV can do (to one decimal place)arrow_forwardA regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y = 26.699 -0.639*x R² = 0.5 r = -0.704 Predict the number of situps a person who watches 6 hours of TV can do (round your answer to three decimal places).arrow_forward
- Use B = -15.812961, and ₁ = 0.096300 to determine the equation of the estimated regression line. (Round your numerical answers to four decimal places.) ŷ =arrow_forwardA regression analysis was performed to determine if there is a relationship between hours of TV watched per day (x) and number of sit ups a person can do (y ). The results of the regression were: y=ax+b a=-1.33 b=25.138 r2=0.712336 r=-0.844 Use this to predict the number of sit ups a person who watches 10 hours of TV can do, and please round your answer to a whole number.arrow_forwardThis is a regression model of how many potato chips one can eat while watching a movie: Y=-2.014*x+40 and the R squared is 0.5 How many chipsp are to be eaten in a 12 hour period?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman