A study was done to determine whether or not social exclusion causes “real pain.” Researchers looked at a random sample of 7 individuals and measured brain activity in an area of the brain that responds to physical pain to see if activity increases as distress from social exclusion increases (measured by social distress score). The social distress scores in the experiment ranged from 0 to 10. A scatterplot shows a moderately strong linear relationship. The least squares regression line is has a slope of 0.06078 and an intercept of -0.1261. A person has a social distress score of 2.0 and a brain activity level of 0.15. What is their residual? **Exploring the Impact of Social Exclusion on Brain Activity**### Study OverviewResearchers aimed to investigate whether social exclusion induces "real pain." They conducted a study with a random sample of 7 individuals. They measured brain activity in a region that responds to physical pain, to assess if this activity increases with higher levels of social distress (quantified by a social distress score). Social distress scores varied from 0 to 10.### Data AnalysisA scatterplot of the data indicated a moderately strong linear relationship between social distress scores and brain activity levels. Using least squares regression analysis, the researchers derived a regression line with:- **Slope:** 0.06078- **Intercept:** -0.1261### Problem StatementGiven:- A person with a social distress score of 2.0- A corresponding brain activity level of 0.15**Question:** What is their residual?### Residual CalculationResiduals measure the difference between observed and predicted values. To find the residual for this individual:1. **Calculate the Predicted Value:** \[ \text{Predicted brain activity} = (\text{Slope} \times \text{Social Distress Score}) + \text{Intercept} \] \[ \text{Predicted brain activity} = (0.06078 \times 2.0) + (-0.1261) \] \[ \text{Predicted brain activity} = 0.12156 - 0.1261 \] \[ \text{Predicted brain activity} = -0.00454 \]2. **Calculate the Residual:** \[ \text{Residual} = \text{Observed brain activity} - \text{Predicted brain activity} \] \[ \text{Residual} = 0.15 - (-0.00454) \] \[ \text{Residual} = 0.15 + 0.00454 \] \[ \text{Residual} = 0.15454 \]**Answer Options:**- a. -0.00454- b. -0.15454- c. 0.14546- d. 0.15000- e. 0.15454**Correct Answer:** e. 0.15454

From the given information, Sample size (n) =7 Least square regression slope (b1) = 0.06078…

Answered: A study was done to determine whether…

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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A study was done to determine whether or not social exclusion causes “real pain.” Researchers looked at a random sample of 7 individuals and measured brain activity in an area of the brain that responds to physical pain to see if activity increases as distress from social exclusion increases (measured by social distress score). The social distress scores in the experiment ranged from 0 to 10. A scatterplot shows a moderately strong linear relationship. The least squares regression line is has a slope of 0.06078 and an intercept of -0.1261. A person has a social distress score of 2.0 and a brain activity level of 0.15. What is their residual?

**Exploring the Impact of Social Exclusion on Brain Activity**

### Study Overview
Researchers aimed to investigate whether social exclusion induces "real pain." They conducted a study with a random sample of 7 individuals. They measured brain activity in a region that responds to physical pain, to assess if this activity increases with higher levels of social distress (quantified by a social distress score). Social distress scores varied from 0 to 10.

### Data Analysis
A scatterplot of the data indicated a moderately strong linear relationship between social distress scores and brain activity levels. Using least squares regression analysis, the researchers derived a regression line with:

- **Slope:** 0.06078
- **Intercept:** -0.1261

### Problem Statement
Given:
- A person with a social distress score of 2.0
- A corresponding brain activity level of 0.15

**Question:** What is their residual?

### Residual Calculation
Residuals measure the difference between observed and predicted values. To find the residual for this individual:

1. **Calculate the Predicted Value:**
\[ \text{Predicted brain activity} = (\text{Slope} \times \text{Social Distress Score}) + \text{Intercept} \]
\[ \text{Predicted brain activity} = (0.06078 \times 2.0) + (-0.1261) \]
\[ \text{Predicted brain activity} = 0.12156 - 0.1261 \]
\[ \text{Predicted brain activity} = -0.00454 \]

2. **Calculate the Residual:**
\[ \text{Residual} = \text{Observed brain activity} - \text{Predicted brain activity} \]
\[ \text{Residual} = 0.15 - (-0.00454) \]
\[ \text{Residual} = 0.15 + 0.00454 \]
\[ \text{Residual} = 0.15454 \]

**Answer Options:**
- a. -0.00454
- b. -0.15454
- c. 0.14546
- d. 0.15000
- e. 0.15454

**Correct Answer:** e. 0.15454

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