QuestionA 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: where x is the number of years of schooling completed and 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 tends to decrease by 3 . When amount of schooling increases by one year, the number of pregnancies tends to increase by 3 . When amount of schooling increases by one year, the number of pregnancies tends to increase by 4 . When amount of schooling increases by one year, the number of pregnancies tends to decrease by 4 .
Studdy Solution
STEP 1
What is this asking?
How does the number of pregnancies change when years of schooling goes up by one?
Watch out!
Don't mix up the slope and the y-intercept!
We're looking at *changes*, so focus on the slope.
STEP 2
1. Understand the Equation
2. Interpret the Slope
STEP 3
Alright, so we've got this cool equation, .
This tells us how the number of pregnancies () changes based on the years of schooling ().
It's a **linear equation**, which means it's a straight line!
STEP 4
Remember, a linear equation is in the form .
Here, is the **slope** (how steep the line is) and is the **y-intercept** (where the line crosses the y-axis).
STEP 5
Let's match our equation, , to the general form.
Notice, we can rewrite our equation as .
Now, it's super clear that our **slope** is and our **y-intercept** is .
STEP 6
The **slope** tells us how much (number of pregnancies) changes when (years of schooling) increases by **one**.
In our case, the slope is .
STEP 7
A **negative slope** means that as increases, *decreases*.
So, as years of schooling increase, the number of pregnancies *decreases*.
STEP 8
Specifically, our slope is .
This means that for every **one** year increase in schooling, the number of pregnancies tends to decrease by **3**.
Boom!
STEP 9
The correct interpretation is: When the amount of schooling increases by one year, the number of pregnancies tends to decrease by 3.
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