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 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 4 10 14 19 29 31 33 D Temperature 55 31 27 -1 - 27 - 41 - 54 a. Find the explained variation. (Round to two decimal places as needed.) b. Find the unexplained variation. (Round to five decimal places as needed.) c. Find the indicated prediction interval. °F

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**Altitude and Temperature Correlation Analysis**

Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. 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 (thousands of feet) | 4  | 10 | 14 | 19 | 29 | 31 | 33 |
|------------------------------|----|----|----|----|----|----|----|
| Temperature (°F)             | 55 | 31 | 27 | -1 | -27 | -41 | -54 |

### Questions
a. **Find the explained variation.**
   - [Input field for explained variation]
   - (Round to two decimal places as needed.)

b. **Find the unexplained variation.**
   - [Input field for unexplained variation]
   - (Round to five decimal places as needed.)

c. **Find the indicated prediction interval.**
   - [Input field for prediction interval]
   - (Round to four decimal places as needed.)
 
\[ ^\circ F < y < ^\circ F \]

### Instructions
1. Enter the explained variation (a) in the respective input field, ensuring values are rounded to two decimal places.
2. Enter the unexplained variation (b) in the respective input field, ensuring values are rounded to five decimal places.
3. For the prediction interval (c), input the lower and upper bounds of the temperature prediction interval, rounding to four decimal places.

### Explanation of Graphs and Diagrams
- **Temperature vs. Altitude Table**: The table provides temperature values at various altitudes during the flight. The first row lists altitudes in thousands of feet, and the second row lists corresponding temperatures in degrees Fahrenheit.

These data are used to analyze and validate a linear correlation between altitude and temperature. The goal is to determine how temperature changes with altitude and use this relationship for prediction within a 95% confidence interval at a specified altitude.

**Note:** It is important to perform the calculations step-by-step, based on statistical methods such as regression analysis, to accurately determine the explained variation, unexplained variation, and prediction interval.
Transcribed Image Text:**Altitude and Temperature Correlation Analysis** Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. 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 (thousands of feet) | 4 | 10 | 14 | 19 | 29 | 31 | 33 | |------------------------------|----|----|----|----|----|----|----| | Temperature (°F) | 55 | 31 | 27 | -1 | -27 | -41 | -54 | ### Questions a. **Find the explained variation.** - [Input field for explained variation] - (Round to two decimal places as needed.) b. **Find the unexplained variation.** - [Input field for unexplained variation] - (Round to five decimal places as needed.) c. **Find the indicated prediction interval.** - [Input field for prediction interval] - (Round to four decimal places as needed.) \[ ^\circ F < y < ^\circ F \] ### Instructions 1. Enter the explained variation (a) in the respective input field, ensuring values are rounded to two decimal places. 2. Enter the unexplained variation (b) in the respective input field, ensuring values are rounded to five decimal places. 3. For the prediction interval (c), input the lower and upper bounds of the temperature prediction interval, rounding to four decimal places. ### Explanation of Graphs and Diagrams - **Temperature vs. Altitude Table**: The table provides temperature values at various altitudes during the flight. The first row lists altitudes in thousands of feet, and the second row lists corresponding temperatures in degrees Fahrenheit. These data are used to analyze and validate a linear correlation between altitude and temperature. The goal is to determine how temperature changes with altitude and use this relationship for prediction within a 95% confidence interval at a specified altitude. **Note:** It is important to perform the calculations step-by-step, based on statistical methods such as regression analysis, to accurately determine the explained variation, unexplained variation, and prediction interval.
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