1) U.S. News & World Report publishes the average starting salary and the average GMAT score for MBA graduates at each of the top 80 ranked schools in the country. The data fit the following regression line:

Y = 288X - 111,408 where X is the average GMAT score for students at a school and Y is the average starting salary for graduates from that same school.

What is a proper interpretation of the coefficient 288 in the regression equation?

A) Average salary will be within plus or minus $288 from $111,408

B) For each additional point in the average GMAT for a school, the average salary of the graduates from that school tends to be $288 higher

C) If a graduate of a school improves her/his GMAT by an additional point, he/she will make $288 more in salary

2) Consider the following two variables:

X = Length of hospital stay by any given patient (days)

Y = Cost of the patient's hospital stay (dollars)

What do you expect about the relationship between these variables?

A) Strong positive correlation, and we expect longer stays to cause higher hospitalization costs for patients with similar illnesses

B) Strong positive correlation, and we expect higher costs to cause longer stays for patients

C) Strong positive correlation, but no causation between them

***Please explain how you arrived at answer***

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1) B) For each additional point in the average GMAT for a school, the average salary of the graduates from that school tends to be $288 higher

2) A) Strong positive correlation, and we expect longer stays to cause higher hospitalization costs for patients with similar illnesses

Explanation:

1) Note 288 is the slope of the regression equation. and the slope is interpreted as change in Y as a result of unit change in X.

In this caseaverage GMAT score for students at a school and Y is the average starting salary for graduates from that same school.

Therefore the right interpretation is given by B.

(Note that c s incorrect since it talks about a graduate instead of score for all students)

2) Note that apart from correlation, its obvious the longer an individual stays in a hospital the higher the cost the will be charged for the stay.

In other words, we can say long stays in a hospital causes high charges. hence the correct solution for the question is A

(note that part A B is incorrect since its not higher cost that cause long stays but its long stay that cause high cost. Past C is incorrect since it ignores causation)

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