Question

"Data from the World Health Organization in 2013 were used to predict the life expectancy of men in a country from the life expectancy of women in that country. The resulting regression equation was ŷ= 3.73 + 0.88(X). Using the regression equation, what would be the predicted life expectancy of men in a country in which the life expectancy of women is 70 years?"

Answer 1

The predicted life expectancy of men in a country in which the life expectancy of women is 70 years is 65.33 years.

Explanation:

The least square regression line is used to predict the value of the dependent variable from an independent variable.

The general form of a least square regression line is:

`\hat y=\alpha +\beta x`

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

The regression line to predict the life expectancy of men in a country from the life expectancy of women in that country is:

`\hat y=3.73 +0.88 x`

Compute the life expectancy of men in a country in which the life expectancy of women is 70 years as follows:

`\hat y=3.73 +0.88 x`

`=3.73 +(0.88* 70)\\=3.73+61.6\\=65.33`

Thus, the predicted life expectancy of men in a country in which the life expectancy of women is 70 years is 65.33 years.