Question

1. the table at the right shows the life expectancy and annual per capita (per person) income for ten countries in south america.

a. graph the data below. choose a good scale for the axes.
b. find a regression line for the data.
\\( y = 0.0004941 x + 68.91 \\)
c. based on an income of $7100, what does the regression equation predict for the life expectancy in ecuador?

d. how much does this differ from the actual value?

e. would you expect a country with a strong public health system to be above or below the regression line? explain.

Explanation:

Step1: Substitute \(x = 7100\) into the regression equation \(y=0.0004941x + 68.91\)

$$y=0.0004941\times7100+68.91$$

Step2: Calculate the product \(0.0004941\times7100\)

$$0.0004941\times7100 = 3.50811$$

Step3: Calculate the sum \(3.50811+68.91\)

$$3.50811 + 68.91=72.41811\approx72.42$$

Step4: Find the difference between the predicted value and the actual value

The actual value for Ecuador is \(77\). The difference is \(77 - 72.42 = 4.58\)

Step5: Analyze the position of a country with a strong public - health system

A strong public - health system would likely lead to a higher life expectancy for a given income level. So, we would expect a country with a strong public health system to be above the regression line.

Answer:

c. The regression equation predicts a life expectancy of approximately \(72.42\)
d. The difference from the actual value (\(77\)) is \(4.58\)
e. Above the regression line. A strong public - health system would increase life expectancy for a given income, so the data point (life expectancy vs income) would be above the line that represents the general trend of life expectancy based on income.