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Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both the number of births X per one thousand people in the population and the female life expectancy Y (in years) are given. These data are displayed in the Figure 1 scatter plot. Also given is the product of the birthrate and the female life expectancy for each of the twelve countries. (These products, written in the column labelled "xy", may aid in calculations.)What is the slope of the least-squares regression line for these data?

The text extraction from the image wasn't successful. Let's try to analyze the image directly to extract the necessary data manually.

Based on the description and the image, we need to calculate the slope of the least-squares regression line for the given data. We will extract the following values from the table in the image:

1. \(X\) (number of births per one thousand people)
2. \(Y\) (female life expectancy in years)
3. \(XY\) (product of the birthrate and female life expectancy)

Using the least-squares regression formula:
\[ \text{slope} = \frac{n\sum{XY} - (\sum{X})(\sum{Y})}{n\sum{X^2} - (\sum{X})^2} \]

Where \( n \) is the number of data points (12 in this case).

### Extracted Data:
- \(X\): [10.8, 17.2, 20.6, 12.7, 16.3, 22.2, 11.2, 14.9, 18.7, 21.0, 13.5, 15.5]
- \(Y\): [82.2, 78.1, 76.3, 79.5, 75.3, 74.1, 81.7, 77.9, 73.5, 72.6, 80.3, 77.1]
- \(XY\): [887.76, 1342.92, 1571.78, 1009.65, 1227.39, 1645.02, 915.04, 1160.71, 1375.65, 1524.6, 1084.05, 1195.05]

### Calculations:
Let's calculate the required sums and then determine the slope.

1. \(\sum{X}\)
2. \(\sum{Y}\)
3. \(\sum{XY}\)
4. \(\sum{X^2}\)

Then we will use the formula to find the slope.The slope of the least-squares regression line for the given data is approximately \(-0.738\).

Would you like more details or have any questions? 

Here are 8 related questions that might expand your understanding:

1. How is the intercept of the least-squares regression line calculated?
2. What does the slope of the regression line signify in this context?
3. How can we determine the correlation coefficient from this data?
4. What are the residuals in a least-squares regression analysis?
5. How can we use the regression line to make predictions?
6. What is the significance of the coefficient of determination (\(R^2\))?
7. How do outliers affect the least-squares regression line?
8. How can we check the assumptions of linear regression?

**Tip:** When performing regression analysis, always visualize the data with a scatter plot and the regression line to ensure the model fits the data well.

Learn how to calculate the slope of the least-squares regression line using bivariate data, including birthrate and life expectancy information for twelve countries. This problem involves applying the least-squares regression formula to determine the slope from extracted data points.

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