Might we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y =81.68 – 0.47x. Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 85 50.7 54.3 46.1 56.5 80- 75- 18.3 72.7 26.1 73.3 70 13.8 72.4 65. 27.5 71.9 60- 49.8 60.0 55 15.2 75.0 50- 32.0 62.3 20 23 30 3 55 60 50 34.6 65.8 49.7 61.5 Birthrate (number of births per 1000 people) 40.4 65.4 Send data to calculator Based on the sample data and the regression line, complete the following. (a) For these data, birthrates that are greater than the mean of the birthrates tend to be paired with female life expectancies that are (Choose one) v the mean of the female life expectancies. (b) According to the regression equation, for an increase of one (birth per 1000 people) in birthrate, there is a corresponding decrease of how many years in female life expectancy? Female life expectancy (in years)
Might we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y =81.68 – 0.47x. Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 85 50.7 54.3 46.1 56.5 80- 75- 18.3 72.7 26.1 73.3 70 13.8 72.4 65. 27.5 71.9 60- 49.8 60.0 55 15.2 75.0 50- 32.0 62.3 20 23 30 3 55 60 50 34.6 65.8 49.7 61.5 Birthrate (number of births per 1000 people) 40.4 65.4 Send data to calculator Based on the sample data and the regression line, complete the following. (a) For these data, birthrates that are greater than the mean of the birthrates tend to be paired with female life expectancies that are (Choose one) v the mean of the female life expectancies. (b) According to the regression equation, for an increase of one (birth per 1000 people) in birthrate, there is a corresponding decrease of how many years in female life expectancy? Female life expectancy (in years)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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#### Questions
**(a)** Based on the sample data and the regression line, complete the following:
For these data, birthrates that are greater than the mean of the birthrates tend to be paired with female life expectancies that are
- **Choose one:**
- Below the mean
- Above the mean
- About the same as
the mean of the female life expectancies.
**(b)** According to the regression equation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe18978a5-daed-417b-bda5-fb0188242e22%2F45e34601-2334-4025-b5c1-c888b9846b77%2Fg9yegx9_processed.png&w=3840&q=75)
Transcribed Image Text:### Predicting Life Expectancies from Birthrates
#### Analysis of Bivariate Data
Below are bivariate data providing information on birthrate and life expectancy for twelve different countries. For each country, both \(x\), the number of births per 1000 people in the population, and \(y\), the female life expectancy (in years), are given. Additionally, the scatter plot for the data and the least-squares regression line are provided. The equation for this line is \( \hat{y} = 81.68 - 0.47x \).
##### Data Table
| Birthrate, \( x \) (number of births per 1000 people) | Female life expectancy, \( y \) (in years) |
|------------------------------------------------------|--------------------------------------------|
| 50.7 | 54.3 |
| 46.1 | 56.5 |
| 18.3 | 72.7 |
| 26.1 | 73.3 |
| 13.8 | 72.4 |
| 27.5 | 71.9 |
| 49.8 | 60.0 |
| 15.2 | 75.0 |
| 32.0 | 62.3 |
| 34.6 | 65.8 |
| 49.7 | 61.5 |
| 40.4 | 65.4 |
##### Scatter Plot Explanation
The scatter plot depicts the relationship between birthrate (number of births per 1000 people) on the x-axis and female life expectancy (in years) on the y-axis. Each point on the graph represents a country. The negative slope of the regression line indicates an inverse relationship between birthrate and female life expectancy; as the birthrate increases, the female life expectancy tends to decrease.
#### Questions
**(a)** Based on the sample data and the regression line, complete the following:
For these data, birthrates that are greater than the mean of the birthrates tend to be paired with female life expectancies that are
- **Choose one:**
- Below the mean
- Above the mean
- About the same as
the mean of the female life expectancies.
**(b)** According to the regression equation
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