At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatter plot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word "strong" in the description of the association? (A) A least-squares model predicts that the more baggage items that are unloaded from a flight, the greater the time required to deliver the items to the baggage claim area. (B) The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model. (C) The time required to deliver an item to the baggage claim area is relatively constant, regardless of the number of baggage items unloaded from a flight. (D) The variability in the time required to deliver all items to the baggage claim area is about the same for all flights, regardless of the number of items unloaded from a flight. (E) The time required to unload baggage items from a flight is related to the time required to deliver the items to the baggage claim area.

Question

30-09-2019
Mathematics

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At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatter plot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word "strong" in the description of the association? (A) A least-squares model predicts that the more baggage items that are unloaded from a flight, the greater the time required to deliver the items to the baggage claim area. (B) The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model. (C) The time required to deliver an item to the baggage claim area is relatively constant, regardless of the number of baggage items unloaded from a flight. (D) The variability in the time required to deliver all items to the baggage claim area is about the same for all flights, regardless of the number of items unloaded from a flight. (E) The time required to unload baggage items from a flight is related to the time required to deliver the items to the baggage claim area.

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rodolforodriguezr rodolforodriguezr · Answer 1 · 2019-10-09T01:50:17+02:00

Answer:

(A): A least-squares model predicts that the more baggage items that are unloaded from a flight, the greater the time required to deliver the items to the baggage claim area.

Step-by-step explanation:

When a least squares regression line is used to try and predict the behavior of a variable y based on observations (x1,y1), (x2,y2),...(xn,yn) of values of y when values of x1, x2,..., xn of another variable x changes, an equation of the form

y = mx + b

is established to help predict the value of y for a given value of x that might not be among the values x1, x2,..., xn used to derive the model.

If the linear model prove to be the most appropriate, then you can have either a positive linear association or a negative linear association.

A positive linear association means that the slope of the line is positive (m>0), so the values of y will increase if the values of x do.

In this case, the variable x is how many baggage items were unloaded from each flight upon arrival, and the variable y is the time required to deliver all the baggage items on the flight to the baggage claim area.

As the linear association is positive, it means

(A): A least-squares model predicts that the more baggage items that are unloaded from a flight, the greater the time required to deliver the items to the baggage claim area.