Bivariate data obtained for the paired variables x and y are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y =-4.87+1.06x . In the "Calculations" tabl Dn : calculations involving the observed y values, the mean y of these values, and the values predicted from the regrecsion equation. Sample data Calculations 160+ 6-G-6ー y 150+ 111.4 115.6 318.9796 409.9005 5.6930 140 122.2 121.5 143.0416 77.4048 9.9982 132.0 139.8 40.1956 2.5281 22.5625 130+ 138.6 130.1 11.2896 73.7194 142.7069 120-- 151.1 160.3 720.3856 476.8109 25.0400 110- Column 1233.8920 1040.3637 206.0007 sums 110 120 130 140 150 160 Send data to Excel Figure 1 Answer the following: 1. The variation in the sample y values that is not explained by the estimated linear v, which for these relationship between x and y is given by the ? data is ? 2. The value r is the proportion of the total variation in the sample y values that is explained by the estimated linear relationship between x and y. For these data, the value of r isO. (Round your answer to at least 2 decimal places.) 3. For the data point (122.2, 121.5), the value of the residual is . (Round your answer to at least 2 decimal places.) 4. The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the v, which for these data is ?
Bivariate data obtained for the paired variables x and y are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y =-4.87+1.06x . In the "Calculations" tabl Dn : calculations involving the observed y values, the mean y of these values, and the values predicted from the regrecsion equation. Sample data Calculations 160+ 6-G-6ー y 150+ 111.4 115.6 318.9796 409.9005 5.6930 140 122.2 121.5 143.0416 77.4048 9.9982 132.0 139.8 40.1956 2.5281 22.5625 130+ 138.6 130.1 11.2896 73.7194 142.7069 120-- 151.1 160.3 720.3856 476.8109 25.0400 110- Column 1233.8920 1040.3637 206.0007 sums 110 120 130 140 150 160 Send data to Excel Figure 1 Answer the following: 1. The variation in the sample y values that is not explained by the estimated linear v, which for these relationship between x and y is given by the ? data is ? 2. The value r is the proportion of the total variation in the sample y values that is explained by the estimated linear relationship between x and y. For these data, the value of r isO. (Round your answer to at least 2 decimal places.) 3. For the data point (122.2, 121.5), the value of the residual is . (Round your answer to at least 2 decimal places.) 4. The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the v, which for these data is ?
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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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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### Questions:
1. **Total Variation (Unexplained Variation):**
The variation in the sample \( y \) values that is **not** explained by the estimated linear relationship between \( x \) and \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb775692f-fc21-4759-89ef-f204cf9eb0c7%2Fd2ee4634-3588-427a-b679-ac2083dde218%2Fcetf0kx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content:**
### Bivariate Data Analysis
**Sample Data:**
The table below shows paired variables \( x \) and \( y \). These data are visualized in Figure 1, where they are plotted on a scatter plot along with the least-squares regression line for the data. The equation for this regression line is \( \hat{y} = -4.87 + 1.06x \).
**Data Table & Calculations:**
| \( x \) | \( y \) | \( (y - \bar{y})^2 \) | \( (\hat{y} - \bar{y})^2 \) | \( (y - \hat{y})^2 \) |
|:------:|:------:|:---------:|:---------:|:---------:|
| 111.4 | 115.6 | 318.9796 | 409.9005 | 5.6930 |
| 122.2 | 121.5 | 143.0416 | 77.4048 | 9.9822 |
| 132.0 | 139.8 | 40.1956 | 2.5281 | 22.5625 |
| 138.6 | 130.0 | 11.2896 | 73.7194 | 142.7069 |
| 151.1 | 160.3 | 220.3856 | 476.8109 | 25.0400 |
| **Column sums** | | **1233.8920** | **1040.3637** | **206.0007** |
**Graphical Representation:**
- **Figure 1:** Shows a scatter plot of the values of \( x \) and \( y \). The plot includes the least-squares regression line derived from these data, which follows the equation \( \hat{y} = -4.87 + 1.06x \).
### Questions:
1. **Total Variation (Unexplained Variation):**
The variation in the sample \( y \) values that is **not** explained by the estimated linear relationship between \( x \) and \(
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