8. The table shown gives the national average pupil-teacher ratio in public schools over selected years. a. Find the equation for the least squares line. Let x correspond to the number of years since 1991 and let y correspond to the average number of pupils per 1 teacher. b. Use the answer from part (a) to predict the pupil-teacher ratio in 2020. Does this seem Year Ratio 1991 17.4 1994 17.7 1997 16.9 realistic? 2000 16.2 c. Calculate and interpret the correlation coefficient. 2003 15.8 a. The equation for the least squares line is Y = (Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.) b. Using the answer from part (a), the pupil-teacher ratio in 2020 will be (Round to one decimal place as needed.) Does this seem realistic? No Yes c. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to four decimal places as needed.) A. The correlation coefficient is which indicates a strong linear correlation. B. The correlation coefficient is which indicates that there is no linear correlation.
8. The table shown gives the national average pupil-teacher ratio in public schools over selected years. a. Find the equation for the least squares line. Let x correspond to the number of years since 1991 and let y correspond to the average number of pupils per 1 teacher. b. Use the answer from part (a) to predict the pupil-teacher ratio in 2020. Does this seem Year Ratio 1991 17.4 1994 17.7 1997 16.9 realistic? 2000 16.2 c. Calculate and interpret the correlation coefficient. 2003 15.8 a. The equation for the least squares line is Y = (Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.) b. Using the answer from part (a), the pupil-teacher ratio in 2020 will be (Round to one decimal place as needed.) Does this seem realistic? No Yes c. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to four decimal places as needed.) A. The correlation coefficient is which indicates a strong linear correlation. B. The correlation coefficient is which indicates that there is no linear correlation.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Educational Website Content**
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**National Average Pupil-Teacher Ratio in Public Schools**
The table provided illustrates the national average pupil-teacher ratio in public schools for selected years. The goal is to calculate and interpret various statistical measures based on the data.
### Table: Year and Pupil-Teacher Ratio
| Year | Ratio |
|------|-------|
| 1994 | 17.7 |
| 1997 | 16.9 |
| 2000 | 16.0 |
| 2003 | 15.2 |
### Task:
1. **Equation for the Least Squares Line**:
- Calculate the equation of the least squares line using the years as variables. Let \( x = 0 \) represent 1994. Use integers or decimals as needed for precision.
2. **Prediction for 2020**:
- Using the least squares equation calculated, predict the pupil-teacher ratio for the year 2020. Round the result to one decimal place.
- **Does this prediction seem realistic?**
- Options:
- ○ Yes
- ○ No
3. **Correlation Coefficient**:
- Calculate and interpret the correlation coefficient. This is a measure of the strength and direction of the linear relationship between the years and the pupil-teacher ratio.
- **Select the correct interpretation**:
- ○ A: The correlation coefficient is ________, indicating a strong linear correlation.
- ○ B: The correlation coefficient is ________, indicating no linear correlation.
**Instructions**: Complete the calculations as described and fill in the appropriate answers, rounding decimals to four decimal places as needed.
---
This content aims to help students apply mathematical concepts of linear regression and correlation to real-world educational data scenarios.
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