A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study are contained in the Excel Online file below. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker. Construct a spreadsheet to answer the following questions.
A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study are contained in the Excel Online file below. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker. Construct a spreadsheet to answer the following questions.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study are contained in the Excel Online file below. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker. Construct a spreadsheet to answer the following questions.
![### Regression Analysis: Predicting the Risk of Stroke
#### a. Developing a Regression Equation
Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood-pressure level.
**The regression equation is:**
\[ \text{Risk} = \_ + \_ \times \text{Age} + \_ \times \text{Pressure} \]
(to 2 decimals)
\[ s = \_ \]
(to 3 decimals)
\[ R^2 = \_ \]
(to 3 decimals)
\[ R\text{-sq adj} = \_ \]
(to 3 decimals)
#### b. Adding Independent Variables
Consider adding two independent variables to the model developed in part (a): one for the interaction between age and blood-pressure level, and the other for whether the person is a smoker. Develop an estimated regression equation using these four independent variables.
**The regression equation is:**
\[ \text{Risk} = \_ + \_ \times \text{Age} + \_ \times \text{Pressure} + \_ \times \text{Smoker} + \_ \times \text{AgePress} \]
(to 2 decimals)
\[ s = \_ \]
(to 3 decimals)
\[ R^2 = \_ \]
(to 3 decimals)
\[ R\text{-sq adj} = \_ \]
(to 3 decimals)
#### c. Significance Testing
At a 0.05 level of significance, test to see whether the addition of the interaction term and the smoker variable contribute significantly to the estimated regression equation developed in part (a).
What is the value of the \( F \) test statistic?
\[ \_ \]
(to 4 decimals)
What is the \( p \)-value?
\[ \text{P-value is } \_ \]
(to 4 decimals)
P-value is \(\_ \), so the addition of the two independent variables \[ \text{(is not / is) \] statistically significant.
This exercise helps you understand the process of developing and refining regression models, a key method in predictive statistics, to better understand and influence health outcomes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc3ad949-79b2-4a66-83f9-922936cf2321%2Faca69ec0-9732-4575-8d93-84a933ee3f7c%2Fg6pqphn_processed.png&w=3840&q=75)
Transcribed Image Text:### Regression Analysis: Predicting the Risk of Stroke
#### a. Developing a Regression Equation
Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood-pressure level.
**The regression equation is:**
\[ \text{Risk} = \_ + \_ \times \text{Age} + \_ \times \text{Pressure} \]
(to 2 decimals)
\[ s = \_ \]
(to 3 decimals)
\[ R^2 = \_ \]
(to 3 decimals)
\[ R\text{-sq adj} = \_ \]
(to 3 decimals)
#### b. Adding Independent Variables
Consider adding two independent variables to the model developed in part (a): one for the interaction between age and blood-pressure level, and the other for whether the person is a smoker. Develop an estimated regression equation using these four independent variables.
**The regression equation is:**
\[ \text{Risk} = \_ + \_ \times \text{Age} + \_ \times \text{Pressure} + \_ \times \text{Smoker} + \_ \times \text{AgePress} \]
(to 2 decimals)
\[ s = \_ \]
(to 3 decimals)
\[ R^2 = \_ \]
(to 3 decimals)
\[ R\text{-sq adj} = \_ \]
(to 3 decimals)
#### c. Significance Testing
At a 0.05 level of significance, test to see whether the addition of the interaction term and the smoker variable contribute significantly to the estimated regression equation developed in part (a).
What is the value of the \( F \) test statistic?
\[ \_ \]
(to 4 decimals)
What is the \( p \)-value?
\[ \text{P-value is } \_ \]
(to 4 decimals)
P-value is \(\_ \), so the addition of the two independent variables \[ \text{(is not / is) \] statistically significant.
This exercise helps you understand the process of developing and refining regression models, a key method in predictive statistics, to better understand and influence health outcomes.
Transcribed Image Text:### Data Analysis with XLMinner Analysis ToolPak
This educational worksheet demonstrates how to use XLMinner Analysis ToolPak for conducting Linear Regression analysis. The spreadsheet is organized into three main parts: data input, instant analysis sections, and summary.
### Data Section
This section contains the primary data variables used for analysis:
- **Risk**: This column contains numerical value as risk score.
- **Age**: Represents the age of individuals.
- **Blood Pressure**: Contains blood pressure measurements.
- **Smoker**: Indicates if the individual is a smoker (1 for yes, 0 for no).
- **AgePress**: A calculation field that might be used for other computations.
- **Formula**: Contains place holder `#N/A` indicating cells where the formulas should be applied.
### Part a: Linear Regression Analysis Setup
In this section, the user is instructed to perform Linear Regression analysis using the XLMinner Analysis ToolPak:
1. **Instructions**:
- Delete all text in the shaded area.
- Use the XLMinner Analysis ToolPak to conduct your Linear Regression analysis.
- After deleting all text in this shaded area, set the output range in the ToolPak to the top left cell of this area (J2).
- Your Linear Regression analysis output should fit into this shaded area.
2. **Output**:
- The output of the Linear Regression analysis should be placed here (cells J2 onward).
### Part b: Secondary Linear Regression Analysis Setup
This section is similar to Part a, but performs a different Linear Regression analysis.
1. **Instructions**:
- Delete all text in the shaded area.
- Use the XLMinner Analysis ToolPak to conduct your Linear Regression analysis.
- After deleting all text in this shaded area, set the output range in the ToolPak to the top left cell of this area (J23).
- Your Linear Regression analysis output should fit into this shaded area.
2. **Output**:
- The output of this additional Linear Regression analysis should be placed here (cells J23 onward).
### Part c: Statistical Summary
In this section, the user calculates the statistical significance of the models tested.
1. **Components**:
- **Level of Significance**: Set at 0.05.
- **F test Statistic**: Placeholder `#N/A` for the calculated F value.
- **p-value (to
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Step 1: Given information
VIEWStep 2: Estimate the regression equation used to predict the risk of stroke given age and blood pressure
VIEWStep 3: Estimate a new regression equation by adding interaction between age and pressure and smoker status
VIEWStep 4: Test the significance of the addition of the interaction term and smoker variable in the first model
VIEWSolution
VIEW
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 29 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman