Medical records indicate that people with more education tend to live longer; the correlation is 0.48.
The slope of the linear model that predicts lifespan from years of education suggests that on average
People tend to live 0.8 extra years for each additional year of education they have. The slope of the line that would predict years of education from lifespan is

Question

Quizplus · Accepted Answer

We know that the correlation between education and lifespan is 0.48. Since correlation is defined as the product of the two standardized variables, we can calculate the standard deviation of lifespan (call it sl) in terms of the standard deviation of education (call it ed) as:

0.48 = cov(sl,ed) / (sd(sl) * sd(ed))

The slope of the linear regression line of lifespan on education can be written as:

b(sl|ed) = cov(sl,ed) / var(ed)

To find b(sl|ed), we need to solve for the covariance term in the formula for the correlation:

cov(sl,ed) = 0.48 * (sd(sl) * sd(ed))

Plugging this into the formula for the slope, we get:

b(sl|ed) = 0.48 * (sd(sl) / sd(ed))

From the information given in the problem, we know that b(sl|ed) = 0.8. We can use this to solve for the ratio of the standard deviations:

0.8 = 0.48 * (sd(sl) / sd(ed))
sd(sl) / sd(ed) = 0.8 / 0.48
sd(sl) / sd(ed) = 1.67

Therefore, the slope of the line that predicts education from lifespan is:

b(ed|sl) = cov(ed,sl) / var(sl)
           = (cov(sl,ed) / var(sl))^-1
           = (0.48 / (sd(sl) * sd(ed)))^-1
           = (0.48 / (sd(ed) * 1.67 * sd(ed)))^-1
           = (0.288 / sd(ed)^2)^-1
           = 3.47 / sd(ed)^2

So the slope depends on the standard deviation of education, but we don't have any information in the problem about what that value might be. However, we do know that the slope is positive, since education and lifespan are positively correlated. Therefore, the best answer choice is B.

Medical Records Indicate That People with More Education Tend to Live