In Talia's math class, the students have been challenged to ask a statistical question and then find the data to answer it. Talia's grandparents are aging, but still in good health, and she notices that people she knows seem to be living longer than in previous generations. She wonders if this is generally true and decides to use her math assignment as an opportunity to explore this question. She finds the following data from the United States Center for Disease Control website: Years since 1950 Life Expectancy 68.2 69.7 70.8 73.7 at Birth 0 10 20 30 b) What is the slope of the regression line? 0.737 40 What does the slope mean in this situation? O Predicted life expentancy at birth in 1950 O Predicted number of people born in 1950 O Average increase in number of people born each year a) Use technology to find the linear regression line. (Round to the nearest tenth). y = 0.18x + 68.1 O Average life expentancy at birth per year Average increase in life expentancy at birth per year c) What is the y-intercept of the regression line? 68.1 45 Strong positive correlation O No correlation O Weak negative correlation 75.4 77.8 76.8 77.6 78.7 78.8 What does the y-intercept mean in this situation? OF O Average increase in life expentancy at birth per year Ⓒ Predicted life expentancy at birth in 1950 O Predicted number of people born in 1950 O Average life expentancy at birth per year O Average increase in number of people born each year 50 55 d) Talia was born in 2003. What would be her predicted life expectancy? 77.5 e) Find the correlation coefficient for the data. (Round to the nearest hundredth) 0.98 O Strong negative correlation O Weak positive correlation 0 0° 60 Select the phrase that best describes the correlation that exists between the year of birth and the life expectancy. 64
In Talia's math class, the students have been challenged to ask a statistical question and then find the data to answer it. Talia's grandparents are aging, but still in good health, and she notices that people she knows seem to be living longer than in previous generations. She wonders if this is generally true and decides to use her math assignment as an opportunity to explore this question. She finds the following data from the United States Center for Disease Control website: Years since 1950 Life Expectancy 68.2 69.7 70.8 73.7 at Birth 0 10 20 30 b) What is the slope of the regression line? 0.737 40 What does the slope mean in this situation? O Predicted life expentancy at birth in 1950 O Predicted number of people born in 1950 O Average increase in number of people born each year a) Use technology to find the linear regression line. (Round to the nearest tenth). y = 0.18x + 68.1 O Average life expentancy at birth per year Average increase in life expentancy at birth per year c) What is the y-intercept of the regression line? 68.1 45 Strong positive correlation O No correlation O Weak negative correlation 75.4 77.8 76.8 77.6 78.7 78.8 What does the y-intercept mean in this situation? OF O Average increase in life expentancy at birth per year Ⓒ Predicted life expentancy at birth in 1950 O Predicted number of people born in 1950 O Average life expentancy at birth per year O Average increase in number of people born each year 50 55 d) Talia was born in 2003. What would be her predicted life expectancy? 77.5 e) Find the correlation coefficient for the data. (Round to the nearest hundredth) 0.98 O Strong negative correlation O Weak positive correlation 0 0° 60 Select the phrase that best describes the correlation that exists between the year of birth and the life expectancy. 64
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
![**Statistical Analysis of Life Expectancy Over Time**
In Talia's math class, students are encouraged to explore statistical questions with data. Curious about the increasing longevity in her family, Talia investigates if this trend is general by examining life expectancy data from the United States Center for Disease Control. The data collected since 1950 is as follows:
| Years since 1950 | 0 | 10 | 20 | 30 | 40 | 45 | 50 | 55 | 60 | 64 |
|------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| Life Expectancy at Birth | 68.2 | 69.7 | 70.8 | 73.7 | 75.4 | 77.8 | 76.8 | 77.6 | 78.7 | 78.8 |
### Analysis Process
a) **Linear Regression Line**
Using technology, the linear regression line is calculated and rounded to the nearest tenth:
\[ y = 0.18x + 68.1 \]
b) **Slope of the Regression Line**
The slope of the regression line is \(0.737\).
- **Meaning of the Slope**: Indicates the average increase in life expectancy at birth per year.
c) **Y-intercept of the Regression Line**
The y-intercept is \(68.1\).
- **Meaning of the Y-intercept**: Represents the predicted life expectancy at birth in 1950.
d) **Prediction for 2003**
Talia, born in 2003, has a predicted life expectancy of \(77.6\) years.
e) **Correlation Coefficient**
The correlation coefficient is \(0.98\), indicating:
- **Description of Correlation**: Strong positive correlation between the year of birth and life expectancy.
This investigation highlights how statistical analysis can reveal trends in data over time, providing insights into societal changes such as increased longevity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd65cec20-e50a-495e-bf9b-5a17b6c06d4e%2F03d95d4a-acd4-46ad-a9e5-732e64dcc573%2Fhxbwd0l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Statistical Analysis of Life Expectancy Over Time**
In Talia's math class, students are encouraged to explore statistical questions with data. Curious about the increasing longevity in her family, Talia investigates if this trend is general by examining life expectancy data from the United States Center for Disease Control. The data collected since 1950 is as follows:
| Years since 1950 | 0 | 10 | 20 | 30 | 40 | 45 | 50 | 55 | 60 | 64 |
|------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| Life Expectancy at Birth | 68.2 | 69.7 | 70.8 | 73.7 | 75.4 | 77.8 | 76.8 | 77.6 | 78.7 | 78.8 |
### Analysis Process
a) **Linear Regression Line**
Using technology, the linear regression line is calculated and rounded to the nearest tenth:
\[ y = 0.18x + 68.1 \]
b) **Slope of the Regression Line**
The slope of the regression line is \(0.737\).
- **Meaning of the Slope**: Indicates the average increase in life expectancy at birth per year.
c) **Y-intercept of the Regression Line**
The y-intercept is \(68.1\).
- **Meaning of the Y-intercept**: Represents the predicted life expectancy at birth in 1950.
d) **Prediction for 2003**
Talia, born in 2003, has a predicted life expectancy of \(77.6\) years.
e) **Correlation Coefficient**
The correlation coefficient is \(0.98\), indicating:
- **Description of Correlation**: Strong positive correlation between the year of birth and life expectancy.
This investigation highlights how statistical analysis can reveal trends in data over time, providing insights into societal changes such as increased longevity.
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VIEWStep 2: Compute the linear regression line
VIEWStep 3: State the slope of regression line and its interpretation
VIEWStep 4: State the y-intercept of regression line and its interpretation
VIEWStep 5: Compute predicted life expectancy at birth of year 2003
VIEWStep 6: Compute the correlation coefficient
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