Listed below are altitudes (thousands of feet) and outside air temperatures ("F) recorded during a fight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a lin correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). 34 13 28 23 -3 31 41 Altitude Temperature 36 <-34 - 58 a Find the explained variation. (Round to two decimal places as needed)
Listed below are altitudes (thousands of feet) and outside air temperatures ("F) recorded during a fight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a lin correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). 34 13 28 23 -3 31 41 Altitude Temperature 36 <-34 - 58 a Find the explained variation. (Round to two decimal places as needed)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 4GP
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![Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).
| Altitude | 3 | 7 | 13 | 23 | 28 | 31 | 34 |
|-------------|------|------|-----|-----|-----|-----|-----|
| Temperature | 59 | 36 | 28 | -3 | -34 | -41 | -58 |
a. Find the explained variation.
\[ \_\_\_\_\_\_\_\_\_\_\_\]
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23157fb6-2442-47a5-a201-c815d86cbc5c%2Fb99409f7-8c70-49de-bd9c-46122ca07652%2Fmx3kawf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).
| Altitude | 3 | 7 | 13 | 23 | 28 | 31 | 34 |
|-------------|------|------|-----|-----|-----|-----|-----|
| Temperature | 59 | 36 | 28 | -3 | -34 | -41 | -58 |
a. Find the explained variation.
\[ \_\_\_\_\_\_\_\_\_\_\_\]
(Round to two decimal places as needed.)
![**Educational Instructions: Statistical Analysis**
**a. Find the explained variation.**
- Input Box: [ ]
- Instruction: (Round to two decimal places as needed.)
**b. Find the unexplained variation.**
- Input Box: [ ]
- Instruction: (Round to five decimal places as needed.)
**c. Find the indicated prediction interval.**
- Input Box: [ ] < y < [ ]
- Instruction: (Round to four decimal places as needed.)
---
**Explanation:**
This exercise involves determining various statistical variations and intervals:
- **Explained Variation**: Refers to the portion of the total variation in a dependent variable that is accounted for by the independent variable in a regression model. Calculation usually involves using the R-squared value.
- **Unexplained Variation**: Also known as the residual variation, this is the part of the total variation that is not explained by the regression model. It calculates how much the observed values deviate from the predicted values.
- **Prediction Interval**: Provides a range in which a future observation will fall, with a certain level of confidence. It is broader than a confidence interval, reflecting the variability of individual outcomes.
Ensure the answers are rounded to the specified decimal places for precision and consistency in reporting statistical information.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23157fb6-2442-47a5-a201-c815d86cbc5c%2Fb99409f7-8c70-49de-bd9c-46122ca07652%2Fxfxskww_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Instructions: Statistical Analysis**
**a. Find the explained variation.**
- Input Box: [ ]
- Instruction: (Round to two decimal places as needed.)
**b. Find the unexplained variation.**
- Input Box: [ ]
- Instruction: (Round to five decimal places as needed.)
**c. Find the indicated prediction interval.**
- Input Box: [ ] < y < [ ]
- Instruction: (Round to four decimal places as needed.)
---
**Explanation:**
This exercise involves determining various statistical variations and intervals:
- **Explained Variation**: Refers to the portion of the total variation in a dependent variable that is accounted for by the independent variable in a regression model. Calculation usually involves using the R-squared value.
- **Unexplained Variation**: Also known as the residual variation, this is the part of the total variation that is not explained by the regression model. It calculates how much the observed values deviate from the predicted values.
- **Prediction Interval**: Provides a range in which a future observation will fall, with a certain level of confidence. It is broader than a confidence interval, reflecting the variability of individual outcomes.
Ensure the answers are rounded to the specified decimal places for precision and consistency in reporting statistical information.
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