Jeremy is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below. Brightness Level (x) Hours (y) Click Download CSV to download csv file of data or copy/paste the data into Excel. After downloading the file, you may want to save it as an Excel Workbook. 10+ 9- 8 Hours 7- 6- 5 3 2 1 1 < Previous 10 At C 20 23 25 30 31 34 40 84 86 5.4 5.8 6.3 6.6 6.2 5 4.8 2.2 J 30 40 60 50 Brightness Level 70 80 a. Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the equation. Note the negative sign in the middle of equation. y = 0.0431 90 FX 100 11 x
Jeremy is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below. Brightness Level (x) Hours (y) Click Download CSV to download csv file of data or copy/paste the data into Excel. After downloading the file, you may want to save it as an Excel Workbook. 10+ 9- 8 Hours 7- 6- 5 3 2 1 1 < Previous 10 At C 20 23 25 30 31 34 40 84 86 5.4 5.8 6.3 6.6 6.2 5 4.8 2.2 J 30 40 60 50 Brightness Level 70 80 a. Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the equation. Note the negative sign in the middle of equation. y = 0.0431 90 FX 100 11 x
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
Related questions
Question
![### Battery Life Analysis Based on Screen Brightness
Jeremy is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below.
#### Dataset:
| Brightness Level (x) | 23 | 25 | 30 | 31 | 34 | 40 | 84 | 86 |
|----------------------|-----|-----|-----|-----|-----|-----|-----|-----|
| Hours (y) | 5.4 | 5.8 | 6.3 | 6.6 | 6.2 | 5 | 4.8 | 2.2 |
#### Graph Description:
The graph depicts the relationship between the brightness level of the phone screen and the battery life (in hours). The Y-axis represents the battery life (in hours), ranging from 0 to 10 hours, while the X-axis represents the brightness level, ranging from 0 to 100.
Each blue dot on the graph corresponds to one set of data points from the table above. As the brightness level increases, the general trend shows a decrease in the battery life.
#### Instructions:
Click **Download CSV** to download a CSV file of the data or copy/paste the data into Excel. After downloading the file, you may want to save it as an Excel Workbook.
#### Task:
1. **Equation for Line of Best Fit**:
- Find the equation for the line of best fit.
- Keep at least 4 decimals for each parameter in the equation.
- Note the negative sign in the middle of the equation.
Example input box format:
\[ \hat{y} = \underline{\ \ \ \ } - 0.0431 \times \underline{\ \ \ \ } \quad x \]
This analysis can help users understand the impact of screen brightness on battery life and make informed decisions about their device settings.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1402ae89-ddd6-4d3d-be54-d5c5eea3ccbf%2F59e2aa70-df95-4e31-905a-4402379cca49%2Frjs6yt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Battery Life Analysis Based on Screen Brightness
Jeremy is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below.
#### Dataset:
| Brightness Level (x) | 23 | 25 | 30 | 31 | 34 | 40 | 84 | 86 |
|----------------------|-----|-----|-----|-----|-----|-----|-----|-----|
| Hours (y) | 5.4 | 5.8 | 6.3 | 6.6 | 6.2 | 5 | 4.8 | 2.2 |
#### Graph Description:
The graph depicts the relationship between the brightness level of the phone screen and the battery life (in hours). The Y-axis represents the battery life (in hours), ranging from 0 to 10 hours, while the X-axis represents the brightness level, ranging from 0 to 100.
Each blue dot on the graph corresponds to one set of data points from the table above. As the brightness level increases, the general trend shows a decrease in the battery life.
#### Instructions:
Click **Download CSV** to download a CSV file of the data or copy/paste the data into Excel. After downloading the file, you may want to save it as an Excel Workbook.
#### Task:
1. **Equation for Line of Best Fit**:
- Find the equation for the line of best fit.
- Keep at least 4 decimals for each parameter in the equation.
- Note the negative sign in the middle of the equation.
Example input box format:
\[ \hat{y} = \underline{\ \ \ \ } - 0.0431 \times \underline{\ \ \ \ } \quad x \]
This analysis can help users understand the impact of screen brightness on battery life and make informed decisions about their device settings.
![### Linear Regression and Battery Life: An Educational Guide
**a. Find the equation for the line of best fit.**
To find the equation for the line of best fit, we need to determine the linear relationship between the brightness level of a phone's screen and the battery life in hours. Keeping at least 4 decimals for each parameter in the equation is crucial. Please note the negative sign in the middle of the equation.
\[ \hat{y} = -0.0431x \]
where:
- \( \hat{y} \) represents the predicted battery life in hours
- \( -0.0431 \) is the slope of the regression line
**b. Interpret the slope in context.**
Jeremy should expect:
- **The brightness level goes down by 0.0431 per additional hour.**
This interpretation indicates that for each additional hour of usage, the brightness level should decrease by 0.0431 units.
**c. What does the equation predict for the number of hours the phone will last at a brightness level of 84?**
To predict the number of hours for a brightness level of 84 using the equation \( \hat{y} = -0.0431x \), substitute \( x = 84 \) and solve for \( \hat{y} \).
Ensure to round your answer properly to 1 decimal place.
\[ \hat{y} = -0.0431 \times 84 \]
hours
**d. What is the residual if the phone battery lasts 4.8 hours when the brightness level is 84?**
The residual is the difference between the actual battery life and the predicted battery life. Calculate the predicted battery life using the brightness level of 84 and then find the residual.
\[ \text{Residual} = \text{Actual Battery Life} - \text{Predicted Battery Life} \]
Round your answer properly to 1 decimal place.
\[ \text{Residual} = 4.8 - \hat{y} \]
hours
**Additional Resources:**
For further assistance, you can watch a comprehensive video walkthrough by clicking on the "Video" link provided.
[**Video**]
[**Previous**]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1402ae89-ddd6-4d3d-be54-d5c5eea3ccbf%2F59e2aa70-df95-4e31-905a-4402379cca49%2F24lhuk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Linear Regression and Battery Life: An Educational Guide
**a. Find the equation for the line of best fit.**
To find the equation for the line of best fit, we need to determine the linear relationship between the brightness level of a phone's screen and the battery life in hours. Keeping at least 4 decimals for each parameter in the equation is crucial. Please note the negative sign in the middle of the equation.
\[ \hat{y} = -0.0431x \]
where:
- \( \hat{y} \) represents the predicted battery life in hours
- \( -0.0431 \) is the slope of the regression line
**b. Interpret the slope in context.**
Jeremy should expect:
- **The brightness level goes down by 0.0431 per additional hour.**
This interpretation indicates that for each additional hour of usage, the brightness level should decrease by 0.0431 units.
**c. What does the equation predict for the number of hours the phone will last at a brightness level of 84?**
To predict the number of hours for a brightness level of 84 using the equation \( \hat{y} = -0.0431x \), substitute \( x = 84 \) and solve for \( \hat{y} \).
Ensure to round your answer properly to 1 decimal place.
\[ \hat{y} = -0.0431 \times 84 \]
hours
**d. What is the residual if the phone battery lasts 4.8 hours when the brightness level is 84?**
The residual is the difference between the actual battery life and the predicted battery life. Calculate the predicted battery life using the brightness level of 84 and then find the residual.
\[ \text{Residual} = \text{Actual Battery Life} - \text{Predicted Battery Life} \]
Round your answer properly to 1 decimal place.
\[ \text{Residual} = 4.8 - \hat{y} \]
hours
**Additional Resources:**
For further assistance, you can watch a comprehensive video walkthrough by clicking on the "Video" link provided.
[**Video**]
[**Previous**]
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