Question

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}=4 - 2x) where (x) is the number of years of schooling completed and (y) is the number of pregnancies. the slope of the regression line can best be interpreted in the following way: when amount of schooling increases by one year, the number of pregnancies increases by 4. when amount of schooling increases by one year, the number of pregnancies increases by 2. when amount of schooling increases by one year, the number of pregnancies decreases by 4. when amount of schooling increases by one year, the number of pregnancies decreases by 2.

Explanation:

Step1: Recall the formula of linear regression

The general form of a simple linear regression equation is $\hat{y}=b_0 + b_1x$, where $b_1$ is the slope.

Step2: Identify the slope in the given equation

In the equation $\hat{y}=4 - 2x$, comparing with $\hat{y}=b_0 + b_1x$, we have $b_1=-2$.

Step3: Interpret the slope

The slope $b_1$ represents the change in $\hat{y}$ (number of pregnancies) for a one - unit change in $x$ (years of schooling). Since $b_1=-2$, when $x$ (years of schooling) increases by 1, $\hat{y}$ (number of pregnancies) changes by $-2$. That is, when the amount of schooling increases by one year, the number of pregnancies decreases by 2.

Answer:

When amount of schooling increases by one year, the number of pregnancies decreases by 2.