Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals. The data is displayed below. Height (in) 85 80 75 70 65 60 ● 5 5.5 6 6.5 7 7.5 8 8.5 9 Wrist Circumference (in) Q Excel Output: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations (Intercept) wrist 0.6492 0.4214 Et 0.4021 4.9094 32 Coefficients Standard Error 36.891 7.64 4.9732 Round answers to 4 decimal places. a) Write the equation of best-fit line. y = 36.891 +4.9732 x t-Stat P-value 4.8287 4.0E-5 1.0639 4.6743 6.0E-5 0° DOLL
Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals. The data is displayed below. Height (in) 85 80 75 70 65 60 ● 5 5.5 6 6.5 7 7.5 8 8.5 9 Wrist Circumference (in) Q Excel Output: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations (Intercept) wrist 0.6492 0.4214 Et 0.4021 4.9094 32 Coefficients Standard Error 36.891 7.64 4.9732 Round answers to 4 decimal places. a) Write the equation of best-fit line. y = 36.891 +4.9732 x t-Stat P-value 4.8287 4.0E-5 1.0639 4.6743 6.0E-5 0° DOLL
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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![**Exploring the Relationship Between Wrist Circumference and Height**
Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals. The data is displayed below.
**Graph Explanation:**
The scatter plot graph shows the relationship between wrist circumference (in inches) on the x-axis and height (in inches) on the y-axis for a sample of individuals. Each blue dot represents an individual's data point. A trend line is also displayed, indicating a possible positive correlation between wrist circumference and height, meaning as wrist circumference increases, height tends to increase as well.
**Excel Output:**
The following are the regression statistics derived from the data:
- **Multiple R:** 0.6492
- **R Square:** 0.4214
- **Adjusted R Square:** 0.4021
- **Standard Error:** 4.9094
- **Observations:** 32
**Regression Coefficients:**
| Coefficients | Standard Error | t-Stat | P-value |
|--------------|----------------|--------|---------|
| Intercept | 36.891 | 7.64 | 4.8287 | 4.0E-5 |
| Wrist | 4.9732 | 1.0639 | 4.6743 | 6.0E-5 |
**Analysis:**
- The intercept coefficient is 36.891, suggesting that when wrist circumference is zero, the predicted height is 36.891 inches.
- The wrist coefficient is 4.9732, indicating that for every one-inch increase in wrist circumference, the height increases by approximately 4.9732 inches.
- The R Square value of 0.4214 suggests that approximately 42.14% of the variability in height can be explained by wrist circumference.
**Conclusion:**
Based on this analysis, there is a significant positive correlation between wrist circumference and height.
**Equation of the Best-Fit Line:**
\[ \hat{y} = 36.891 + 4.9732 \cdot x \]
**Instructions:**
Round answers to 4 decimal places where necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1402ae89-ddd6-4d3d-be54-d5c5eea3ccbf%2F6c2ef8a6-4b72-4e59-ad38-83bdaf7bdf4a%2Fysdjq2b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exploring the Relationship Between Wrist Circumference and Height**
Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals. The data is displayed below.
**Graph Explanation:**
The scatter plot graph shows the relationship between wrist circumference (in inches) on the x-axis and height (in inches) on the y-axis for a sample of individuals. Each blue dot represents an individual's data point. A trend line is also displayed, indicating a possible positive correlation between wrist circumference and height, meaning as wrist circumference increases, height tends to increase as well.
**Excel Output:**
The following are the regression statistics derived from the data:
- **Multiple R:** 0.6492
- **R Square:** 0.4214
- **Adjusted R Square:** 0.4021
- **Standard Error:** 4.9094
- **Observations:** 32
**Regression Coefficients:**
| Coefficients | Standard Error | t-Stat | P-value |
|--------------|----------------|--------|---------|
| Intercept | 36.891 | 7.64 | 4.8287 | 4.0E-5 |
| Wrist | 4.9732 | 1.0639 | 4.6743 | 6.0E-5 |
**Analysis:**
- The intercept coefficient is 36.891, suggesting that when wrist circumference is zero, the predicted height is 36.891 inches.
- The wrist coefficient is 4.9732, indicating that for every one-inch increase in wrist circumference, the height increases by approximately 4.9732 inches.
- The R Square value of 0.4214 suggests that approximately 42.14% of the variability in height can be explained by wrist circumference.
**Conclusion:**
Based on this analysis, there is a significant positive correlation between wrist circumference and height.
**Equation of the Best-Fit Line:**
\[ \hat{y} = 36.891 + 4.9732 \cdot x \]
**Instructions:**
Round answers to 4 decimal places where necessary.
![# Linear Regression Analysis: Height vs. Wrist Circumference
In this educational module, you will learn to perform linear regression analysis using height and wrist circumference data.
## Instructions
### Round answers to 4 decimal places.
#### a) Write the equation of the best-fit line.
Using the standard linear regression equation \( \hat{y} = a + bx \):
\[ \hat{y} = 36.891 + 4.9732x \]
#### b) Identify the correlation coefficient.
The correlation coefficient (r) is a measure of the linear relationship between two variables.
\[ r = 0.6492 \]
#### c) What fraction of variability in heights can be explained using the linear model of height vs. wrist circumference?
The coefficient of determination (R²) indicates the fraction of the variance in the dependent variable that is predictable from the independent variable.
\[ \text{Coefficient of determination} = 0.4214 \]
This means that approximately 42.14% of the variability in heights can be explained by the wrist circumference.
#### d) Use the equation of the best-fit line to predict the height of a person with a wrist circumference of 6 inches.
\[ \hat{y} = 36.891 + 4.9732 \times 6 \]
\[ \hat{y} = 36.891 + 29.8392 \]
\[ \hat{y} = 66.7302 \]
So, the predicted height is 66.7302 inches.
#### e) One of the points on the scatterplot is (7.5, 83.7). Calculate the residual for this point. Hint: \( y - \hat{y} \).
1. Calculate the predicted value (\( \hat{y} \)) for \( x = 7.5 \):
\[ \hat{y} = 36.891 + 4.9732 \times 7.5 \]
\[ \hat{y} = 36.891 + 37.299 \]
\[ \hat{y} = 74.19 \]
2. Calculate the residual:
\[ \text{Residual} = y - \hat{y} \]
\[ \text{Residual} = 83.7 - 74.19 \]
\[ \text{Residual} = 9.51 \]
So, the residual for this point is 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1402ae89-ddd6-4d3d-be54-d5c5eea3ccbf%2F6c2ef8a6-4b72-4e59-ad38-83bdaf7bdf4a%2Fd2cfyo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Linear Regression Analysis: Height vs. Wrist Circumference
In this educational module, you will learn to perform linear regression analysis using height and wrist circumference data.
## Instructions
### Round answers to 4 decimal places.
#### a) Write the equation of the best-fit line.
Using the standard linear regression equation \( \hat{y} = a + bx \):
\[ \hat{y} = 36.891 + 4.9732x \]
#### b) Identify the correlation coefficient.
The correlation coefficient (r) is a measure of the linear relationship between two variables.
\[ r = 0.6492 \]
#### c) What fraction of variability in heights can be explained using the linear model of height vs. wrist circumference?
The coefficient of determination (R²) indicates the fraction of the variance in the dependent variable that is predictable from the independent variable.
\[ \text{Coefficient of determination} = 0.4214 \]
This means that approximately 42.14% of the variability in heights can be explained by the wrist circumference.
#### d) Use the equation of the best-fit line to predict the height of a person with a wrist circumference of 6 inches.
\[ \hat{y} = 36.891 + 4.9732 \times 6 \]
\[ \hat{y} = 36.891 + 29.8392 \]
\[ \hat{y} = 66.7302 \]
So, the predicted height is 66.7302 inches.
#### e) One of the points on the scatterplot is (7.5, 83.7). Calculate the residual for this point. Hint: \( y - \hat{y} \).
1. Calculate the predicted value (\( \hat{y} \)) for \( x = 7.5 \):
\[ \hat{y} = 36.891 + 4.9732 \times 7.5 \]
\[ \hat{y} = 36.891 + 37.299 \]
\[ \hat{y} = 74.19 \]
2. Calculate the residual:
\[ \text{Residual} = y - \hat{y} \]
\[ \text{Residual} = 83.7 - 74.19 \]
\[ \text{Residual} = 9.51 \]
So, the residual for this point is 9.
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