30. The regression equation y = 980 + 310x (x = team size, y = budget amount) What is the appropriate interpretation of this equation?
Answer: D
An increase of 1 in the team size is associated with an increase in the budget of $310.
The regression equation indicates that for each additional member added to the team (represented by an increase of 1 in x), the budget (y) increases by $310.
A) An increase of 310 in the team size is associated with an increase in the budget of $1.
This interpretation is incorrect because the regression equation shows that the coefficient of x (team size) is $310, meaning that a unit increase in team size correlates with a $310 increase in budget, not the other way around.
B) An increase of 980 in the team size is associated with an increase in the budget of $1.
This option misinterprets the equation. The constant term of $980 does not represent a change in team size; rather, it indicates the base budget when the team size is zero. Thus, it cannot be interpreted as a relationship between team size and budget.
C) An increase of 1 in the team size is associated with an increase in the budget of $980.
This statement is incorrect as it misrepresents the coefficient of the team size. The correct interpretation is that an increase of 1 in team size leads to an increase of $310 in the budget, not $980.
D) An increase of 1 in the team size is associated with an increase in the budget of $310.
This statement is accurate and correctly reflects the meaning of the regression equation. The coefficient of x is $310, indicating how much the budget increases for each additional team member.
Conclusion
The correct interpretation of the regression equation clearly indicates that an increase of 1 in the team size results in a $310 increase in the budget. All other options fail to accurately represent the relationship defined by the regression coefficients, leading to misunderstandings of the underlying data trends.