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Problem-Solving and Data AnalysisEasyInterpreting the slope of a line of best fit

Problem-Solving and Data Analysis practice question

A scatterplot shows the relationship between years of experience, x, and annual salary, y, in thousands of dollars, for 40 employees at a company. The line of best fit for the data is y = 2.5x + 12.

What does the number 2.5 most likely represent?

  1. A. The predicted increase in annual salary, in thousands of dollars, for each additional year of experience.Correct
  2. B. The predicted annual salary, in thousands of dollars, of an employee with no experience.
  3. C. The number of years of experience needed to earn a salary of 12 thousand dollars.
  4. D. The total annual salary, in thousands of dollars, of all 40 employees.

Answer: A. The predicted increase in annual salary, in thousands of dollars, for each additional year of experience.

In a line of best fit, the coefficient of x is the slope: the predicted change in y for a one-unit increase in x. Here a one-year increase in experience is associated with a predicted 2.5 thousand dollar rise in salary.

Why the other answers are wrong

B. The predicted annual salary, in thousands of dollars, of an employee with no experience.
That is the y-intercept, 12 — the predicted salary when x = 0. 2.5 is attached to x, so it describes change, not a starting value.
C. The number of years of experience needed to earn a salary of 12 thousand dollars.
2.5 is a rate of change in salary, not a count of years. Reading 12 as a salary and solving for x would be a different question.
D. The total annual salary, in thousands of dollars, of all 40 employees.
A line of best fit models an individual's predicted salary from experience, not a sum across all employees.

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