Question

For the regression equation y^=0.08x1.20, where x represents the number of pieces in a set and y^ is the predicted price (in dollars) of a set, 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.
D) When the number of pieces is 0, the predicted price is $0.08.

Answer 1

The meaning of the y-intercept (1.20) in the regression equation y^=0.08x+1.20 is that when the number of pieces in a set is 0, the predicted price of the set is $1.20.

Step-by-step explanation:

Understanding the y-intercept in a Regression Equation

The y-intercept in a regression equation represents the predicted value of y when the independent variable (x) is zero. For the regression equation y^=0.08x+1.20, the y-intercept is 1.20. This indicates that when the number of pieces in a set is 0, the predicted price of the set is $1.20. Option (C), "When the number of pieces is 0, the predicted price is $1.20," best describes the meaning of the y-intercept in this context.

It's important to note that a y-intercept may not always be a practically applicable value. For instance, it wouldn't make sense to have a set with zero pieces in a real-world scenario. However, the y-intercept gives us a starting point for the regression line on the plot.

If you alter the regression equation by changing the y-intercept, this would shift the entire line up or down on the y-axis, affecting all predicted prices. Therefore, the y-intercept is an essential element of the linear model.