Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of a set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. Which statement best describes the meaning of the y-intercept of the regression line?
Answer
A
When the price of a set is $0, the predicted number of pieces is 0.
B
When the price of a set is $0, the predicted number of pieces is 1.20.
C
When the number of pieces is 0, the predicted price is $1.20. This interpretation is not meaningful because a set cannot have 0 pieces.
D
When the number of pieces is 0, the predicted price is $0.08. This interpretation is not meaningful because a set cannot have 0 pieces.
Explanation
The y-intercept is the predicted value of y when x = 0. In the equation ŷ = 0.08x + 1.20, setting the number of pieces to 0 gives a predicted price of $1.20. This is not a meaningful interpretation in context because a set cannot have zero pieces.
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