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Which statement best describes the meaning of the y-intercept of the regression line?

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.

User Sletheren
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1 Answer

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Final answer:

The y-intercept of a regression line, commonly denoted as 'a' or 'b' in the equation y = mx + b, represents the predicted value of y when x is zero. It should provide a sensible starting value for predictions based on the regression, but not all y-intercept values may be meaningful depending on the context of the data set being analyzed.

Step-by-step explanation:

The y-intercept of a regression line is a crucial concept in understanding linear relationships in data. The y-intercept refers to the point where the regression line crosses the y-axis. It provides the value of the dependent variable (y) when the independent variable (x) is zero. This concept is often denoted as 'a' or 'b' in the regression equation (y = mx + b).

Given the context of the question, the statement that best describes the meaning of the y-intercept of a regression line would be the initial value of the predicted dependent variable when the independent variable is zero. For example, if we're talking about a cleaning company that charges an initial fee regardless of the number of hours worked, the y-intercept would represent this initial fee. However, interpretations of the y-intercept should make sense within the context of the data. For instance, predicting a number of pieces when price is $0 might not be sensible if products can't be free or if a product can't have zero pieces.

In scenarios where the interpretation of the y-intercept is not meaningful, such as predicting stock prices when the market is closed (time = 0), it's important to state that the value provided by the y-intercept is not practical in the real-world scenario being studied.

User John Stimac
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