Might we be able to predict life expectancies from birthrates?

Below are bivariate data giving birthrate and lile expectancy information for each of twelve countries. For each of the countries, boths, 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 scaller slot for the data and the least squares topresston tine. The ecuation for this line is y=83.19-0.49x.

Birthrate, x (number of births per 1000 people)

Female life expectancy, F (in years)

28.6

732

318

60.2

517

53.3

73.1

50.0

19.6

759

133

66.9

30.7

586

447

74.1

255

62.8

462

742

148

350

659

Daved.on the sample data and the regression Time, complete the following

( For these data, birthrates that are greater than the mean of the birthrates tend to be paired with female she expectancies that ace! (Choose one) the mean of the female life expectancies.

() 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 fermare life expectancy?

Let's break down the problem step by step.

### Part 1: Birthrates vs. Female Life Expectancies
You have bivariate data with birthrate (\( x \)) and female life expectancy (\( y \)) for twelve countries. The regression line equation is given as:

\[
y = 83.19 - 0.49x
\]

The equation shows that there's a negative relationship between birthrate and female life expectancy, meaning as the birthrate increases, female life expectancy decreases.

#### Question: Birthrates greater than the mean vs. Female Life Expectancies
The question asks whether birthrates greater than the mean are paired with female life expectancies that are above or below the mean.

Since the slope of the regression line (\(-0.49\)) is negative, birthrates greater than the mean tend to be paired with female life expectancies that are **below** the mean. This is because higher birthrates correlate with lower life expectancies.

### Part 2: Interpretation of the Slope
The slope of the regression line is \(-0.49\). This value indicates that for every increase of 1 birth per 1000 people in the birthrate, female life expectancy decreases by 0.49 years.

So, the answer is:
- **For an increase of 1 birth per 1000 people in the birthrate, female life expectancy decreases by 0.49 years.**

### Summary:
- **Birthrates greater than the mean are paired with female life expectancies that are below the mean.**
- **For each 1 birth per 1000 people increase in birthrate, female life expectancy decreases by 0.49 years.**

Would you like a more detailed explanation of these concepts or further exploration of the data? 

### 5 Related Questions:
1. How do outliers in the data affect the regression line?
2. What does the y-intercept (83.19) represent in this context?
3. How might other factors (e.g., GDP per capita) influence the relationship between birthrate and life expectancy?
4. What would be the predicted female life expectancy for a country with a birthrate of 35 births per 1000 people?
5. How does the strength of the correlation affect our confidence in using this model for predictions?

**Tip:** Always check the scatter plot for the data to visually inspect how well the regression line fits the data points. This can give you insight into the reliability of the model.

Explore the relationship between birthrates and female life expectancy using regression analysis. Learn how changes in birthrates impact life expectancy, with practical examples and interpretation of statistical data. Suitable for high school students studying statistics and regression analysis.

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