What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places. (b) What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.

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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.

| Birthrate, \( x \) (number of births per 1000 pop.) | Female life expectancy, \( y \) (in years) |
|---|---|
| 29.2 | 64.5 |
| 27.4 | 71.4 |
| 41.6 | 57.6 |
| 52.2 | 44.8 |
| 41.2 | 60.6 |
| 14.0 | 75.7 |
| 34.8 | 62.6 |
| 14.1 | 71.9 |
| 33.4 | 68.4 |
| 51.2 | 58.9 |
| 47.9 | 62.6 |
| 49.7 | 54.7 |
| 25.7 | 75.2 |

**Scatter Plot Explanation:**

The scatter plot in Figure 1 illustrates the relationship between birthrate (number of births per 1000 population) on the x-axis and female life expectancy (in years) on the y-axis. The data points are plotted as 'x' markers. There is a general downward trend, indicating an inverse relationship between birthrate and life expectancy.

**The least-squares regression line** for these data has a slope of approximately \(-0.47\).

Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a [list of formulas](#)).

(a) What is the value of the **y-intercept** of the least-squares regression line for these data?  
Round your answer to at least two decimal places.

[  ]

(b) What is the value of the **sample correlation coefficient** for these data?  
Round your answer to at least three decimal places.

[  ]
Transcribed Image Text: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. | Birthrate, \( x \) (number of births per 1000 pop.) | Female life expectancy, \( y \) (in years) | |---|---| | 29.2 | 64.5 | | 27.4 | 71.4 | | 41.6 | 57.6 | | 52.2 | 44.8 | | 41.2 | 60.6 | | 14.0 | 75.7 | | 34.8 | 62.6 | | 14.1 | 71.9 | | 33.4 | 68.4 | | 51.2 | 58.9 | | 47.9 | 62.6 | | 49.7 | 54.7 | | 25.7 | 75.2 | **Scatter Plot Explanation:** The scatter plot in Figure 1 illustrates the relationship between birthrate (number of births per 1000 population) on the x-axis and female life expectancy (in years) on the y-axis. The data points are plotted as 'x' markers. There is a general downward trend, indicating an inverse relationship between birthrate and life expectancy. **The least-squares regression line** for these data has a slope of approximately \(-0.47\). Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a [list of formulas](#)). (a) What is the value of the **y-intercept** of the least-squares regression line for these data? Round your answer to at least two decimal places. [ ] (b) What is the value of the **sample correlation coefficient** for these data? Round your answer to at least three decimal places. [ ]
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