Back to Use the equation of a linear model to solve problems in the context of bivariate measurement data — Problem 3 · Task Set 84

Linear Models -- Tutor Intake Assessment

This is a quick check on using the equation of a fitted line: writing it,
interpreting slope and y-intercept in context, and making predictions.
The goal is to see where to focus our first sessions together, not to
grade you. Work independently, without notes.

Grade 8·8 problems·~12 min·Common Core Math - Grade 8·container·8-sp-a-3

Work through problems with immediate feedback

Concepts

A linear model relates a person's age (x, in years, with data
collected from ages 25 to 65) to annual salary (y, in
thousands of dollars): y = 1.2x + 8. A student says, "The
y-intercept of 8 means a newborn (age 0) is predicted to earn
$8,000 per year, and that's a perfectly meaningful prediction."
Is the student correct?

Yes -- the y-intercept always gives a meaningful real-world value

Yes, because $8,000 is a small, reasonable-sounding number

No -- linear models never have meaningful y-intercepts

No -- x = 0 is far outside the data range (ages 25-65) and does not make sense in this context, so the y-intercept is not a meaningful prediction here