The standard deviation of the residuals is s=5.9. Interpret the value in context. **Description:**A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is also shown. The computer output from the least-squares regression analysis is also shown.**Graph Details:**- **Scatterplot:** The graph consists of points plotted on a coordinate plane, representing the relationship between foot length (x-axis) and height (y-axis).- **X-Axis:** Labeled "Foot Length (cm)" ranging from 18 cm to 36 cm.- **Y-Axis:** Labeled "Height (cm)" ranging from 150 cm to 190 cm.- **Data Points:** Individual dots show the foot length and corresponding height of each student.- **Regression Line:** A straight line through the points representing the best fit line calculated through least-squares regression, indicating a positive correlation between foot length and height. **Regression Analysis Result Overview**The table presents the results of a regression analysis, which examines the relationship between foot length and an unspecified dependent variable.| Term | Coef | (SE) Coef | T-Value | P-Value ||--------------|--------|-----------|---------|---------|| Constant | 105.08 | 6.00 | 17.51 | 0.000 || Foot length | 2.599 | 0.238 | 10.92 | 0.000 |- **Constant**: The intercept of the regression line is 105.08, with a standard error (SE) of 6.00. The T-value is 17.51, and the P-value is 0.000, indicating statistical significance. - **Foot length**: This variable has a coefficient of 2.599, meaning each unit increase in foot length is associated with an increase of 2.599 in the dependent variable. The SE is 0.238, T-value is 10.92, and the P-value is 0.000, suggesting strong significance.Additionally, the regression output provides:- **S (Standard Error of the Estimate)**: 5.90181, indicating the typical distance that the observed values fall from the regression line. - **R-squared (R-sq)**: 65.42%, indicating that approximately 65.42% of the variance in the dependent variable is explained by the model.This analysis demonstrates a significant relationship between foot length and the dependent variable.

Name: The standard deviation of the residuals is s=5.9. Interpret the value
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Description: The standard deviation of the residuals is s=5.9. Interpret the value in context. **Description:**A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height

The residual standard deviation 's' is the difference between set of observed and predicted values.…

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Math

Statistics

The standard deviation of the residuals is s=5.9. Interpret the value in context.

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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Question

The standard deviation of the residuals is s=5.9. Interpret the value in context.

**Description:**

A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is also shown. The computer output from the least-squares regression analysis is also shown.

**Graph Details:**

- **Scatterplot:** The graph consists of points plotted on a coordinate plane, representing the relationship between foot length (x-axis) and height (y-axis).
- **X-Axis:** Labeled "Foot Length (cm)" ranging from 18 cm to 36 cm.
- **Y-Axis:** Labeled "Height (cm)" ranging from 150 cm to 190 cm.
- **Data Points:** Individual dots show the foot length and corresponding height of each student.
- **Regression Line:** A straight line through the points representing the best fit line calculated through least-squares regression, indicating a positive correlation between foot length and height.

**Regression Analysis Result Overview**

The table presents the results of a regression analysis, which examines the relationship between foot length and an unspecified dependent variable.

| Term | Coef | (SE) Coef | T-Value | P-Value |
|--------------|--------|-----------|---------|---------|
| Constant | 105.08 | 6.00 | 17.51 | 0.000 |
| Foot length | 2.599 | 0.238 | 10.92 | 0.000 |

- **Constant**: The intercept of the regression line is 105.08, with a standard error (SE) of 6.00. The T-value is 17.51, and the P-value is 0.000, indicating statistical significance.

- **Foot length**: This variable has a coefficient of 2.599, meaning each unit increase in foot length is associated with an increase of 2.599 in the dependent variable. The SE is 0.238, T-value is 10.92, and the P-value is 0.000, suggesting strong significance.

Additionally, the regression output provides:

- **S (Standard Error of the Estimate)**: 5.90181, indicating the typical distance that the observed values fall from the regression line.

- **R-squared (R-sq)**: 65.42%, indicating that approximately 65.42% of the variance in the dependent variable is explained by the model.

This analysis demonstrates a significant relationship between foot length and the dependent variable.

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