**Relationship Between Bicep Girth and Weight: A Statistical Analysis**Based on data from 34 adults who exercise regularly, the line of best fit for the relationship between bicep girth (the length in centimeters around the upper arm) and the person's weight is:\[ \text{predicted weight} = 2.6 \cdot \text{bicep girth} - 10.5 \]where predicted weight is measured in kilograms and bicep girth is measured in centimeters.This linear equation suggests that for each additional centimeter increase in bicep girth, the weight of the person is predicted to increase by 2.6 kilograms. Additionally, the equation intercepts the y-axis at -10.5, which is of less practical significance, as negative weights are not feasible, yet it represents the point where the line crosses the axis when the bicep girth is zero. This type of linear regression analysis is valuable in understanding the correlation between different physical measurements and can be useful in fields like fitness training, health assessment, and physical education. ### Least-Squares Equation Application in Bicep Girth and Predicted Weight Analysis#### Graph DescriptionThe provided graph plots data points representing weight (in kg) versus bicep girth (in cm). Both the x-axis and y-axis are uniformly scaled with the x-axis representing bicep girth ranging from 20 cm to 40 cm, and the y-axis representing weight ranging from 50 kg to 90 kg. A line of best fit is plotted, which indicates a positive correlation between bicep girth and weight.#### Questions and Instructions**A) Complete the table below using the least-squares equation.**| x = bicep girth (in cm) | ŷ = predicted weight (in kg) ||-------------------------|-----------------------------|| 0 | || 20 | || 25 | || 33 | || 45 | |**B) In the equation, when $ x = 0 $, the initial value of $ \hat{y} $ is -10.5. Does this number, -10.5, mean anything about bicep girth or predicted weight? Why or why not?****C) Explain the meaning of the slope of the line of best fit. Tell how the slope relates a person's bicep girth to his or her predicted weight.****D) If the bicep girth of an adult increased by 3 cm, how would that person’s predicted weight change?**### Explanation**B) Interpretation of Initial Value**The initial value of $ \hat{y} $ at $ x = 0 $ is -10.5. Since negative weight is not physically meaningful, this value does not provide a direct real-world interpretation in this context. It simply represents the y-intercept in the regression equation, and can be considered as a mathematical artifact of the model rather than having practical significance.**C) Meaning of the Slope**The slope of the line of best fit represents the rate of change of predicted weight with respect to bicep girth. If the slope is positive, it indicates that as bicep girth increases, the predicted weight also increases. The numerical value of the slope tells us how many kilograms the weight is expected to increase per centimeter increase in bicep girth.**D) Impact of Increased

Name: **Relationship Between Bicep Girth and Weight: A Statistical Analysis
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Description: **Relationship Between Bicep Girth and Weight: A Statistical Analysis**Based on data from 34 adults who exercise regularly, the line of best fit for the relationship between bicep girth (the length in centimeters around the upper arm) and the person

The given line is, predicted weight = 2.6(bicep girth) – 10.5.

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Based on data from 34 adults who exercise regularly, the line of best fit for the relationship between bicep girth (the length in centimeters around the upper arm) and the person's weight is: predicted weight = 2.6 bicep girth – 10.5 %3D where predicted weight is measured in kilograms and bicep girth is measured in centimeters.

Based on data from 34 adults who exercise regularly, the line of best fit for the relationship between bicep girth (the length in centimeters around the upper arm) and the person's weight is: predicted weight = 2.6 bicep girth – 10.5 %3D where predicted weight is measured in kilograms and bicep girth is measured in centimeters.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Question

**Relationship Between Bicep Girth and Weight: A Statistical Analysis**

Based on data from 34 adults who exercise regularly, the line of best fit for the relationship between bicep girth (the length in centimeters around the upper arm) and the person's weight is:

\[ \text{predicted weight} = 2.6 \cdot \text{bicep girth} - 10.5 \]

where predicted weight is measured in kilograms and bicep girth is measured in centimeters.

This linear equation suggests that for each additional centimeter increase in bicep girth, the weight of the person is predicted to increase by 2.6 kilograms. Additionally, the equation intercepts the y-axis at -10.5, which is of less practical significance, as negative weights are not feasible, yet it represents the point where the line crosses the axis when the bicep girth is zero.

This type of linear regression analysis is valuable in understanding the correlation between different physical measurements and can be useful in fields like fitness training, health assessment, and physical education.

### Least-Squares Equation Application in Bicep Girth and Predicted Weight Analysis

#### Graph Description
The provided graph plots data points representing weight (in kg) versus bicep girth (in cm). Both the x-axis and y-axis are uniformly scaled with the x-axis representing bicep girth ranging from 20 cm to 40 cm, and the y-axis representing weight ranging from 50 kg to 90 kg. A line of best fit is plotted, which indicates a positive correlation between bicep girth and weight.

#### Questions and Instructions

**A) Complete the table below using the least-squares equation.**

| x = bicep girth (in cm) | ŷ = predicted weight (in kg) |
|-------------------------|-----------------------------|
| 0 | |
| 20 | |
| 25 | |
| 33 | |
| 45 | |

**B) In the equation, when $ x = 0 $, the initial value of $ \hat{y} $ is -10.5. Does this number, -10.5, mean anything about bicep girth or predicted weight? Why or why not?**

**C) Explain the meaning of the slope of the line of best fit. Tell how the slope relates a person's bicep girth to his or her predicted weight.**

**D) If the bicep girth of an adult increased by 3 cm, how would that person’s predicted weight change?**

### Explanation

**B) Interpretation of Initial Value**
The initial value of $ \hat{y} $ at $ x = 0 $ is -10.5. Since negative weight is not physically meaningful, this value does not provide a direct real-world interpretation in this context. It simply represents the y-intercept in the regression equation, and can be considered as a mathematical artifact of the model rather than having practical significance.

**C) Meaning of the Slope**
The slope of the line of best fit represents the rate of change of predicted weight with respect to bicep girth. If the slope is positive, it indicates that as bicep girth increases, the predicted weight also increases. The numerical value of the slope tells us how many kilograms the weight is expected to increase per centimeter increase in bicep girth.

**D) Impact of Increased

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