Problem
A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: $\hat{y}=1-5 x$ where $\mathrm{x}$ is the number of years of schooling completed and $\mathrm{y}$ is the number of pregnancies. The slope of the regression line can be interpreted in the following way: When amount of schooling increases by one year, the number of pregnancies decreases by 1 . When amount of schooling increases by one year, the number of pregnancies increases by 5 . When amount of schooling increases by one year, the number of pregnancies increases by 1. When amount of schooling increases by one year, the number of pregnancies decreases by 5 .
Solution
Step 1 ：A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: \(\hat{y}=1-5 x\) where \(x\) is the number of years of schooling completed and \(y\) is the number of pregnancies.
Step 2 ：The slope of the regression line is -5. This means that for every unit increase in x (years of schooling), y (number of pregnancies) decreases by 5.
Step 3 ：Final Answer: \(\boxed{\text{When amount of schooling increases by one year, the number of pregnancies decreases by 5.}}\)
