SCENARIO 18-12
The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below:

-Referring to Scenario 18-11,which of the following is the correct interpretation for the Tofel500 slope coefficient?
A)Holding constant the effect of the other variables,the estimated mean value of school type is 0.39 lower when the school has a TOEFL criterion that is at least 550.
B)Holding constant the effect of the other variables,the estimated school type decreases by 0.39 when the school has a TOEFL criterion that is at least 550.
C)Holding constant the effect of the other variables,the estimated natural logarithm of the odds ratio of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not.
D)Holding constant the effect of the other variables,the estimated probability of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not.

Question

SCENARIO 18-12
The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below:

-Referring to Scenario 18-11,which of the following is the correct interpretation for the Tofel500  slope coefficient?
A)Holding constant the effect of the other variables,the estimated mean value of school type is 0.39 lower when the school has a TOEFL criterion that is at least 550. 
B)Holding constant the effect of the other variables,the estimated school type decreases by 0.39 when the school has a TOEFL criterion that is at least 550. 
C)Holding constant the effect of the other variables,the estimated natural logarithm of the odds ratio of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not. 
D)Holding constant the effect of the other variables,the estimated probability of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not.

Quizplus · Accepted Answer

The correct interpretation of a slope coefficient in a logistic regression (which is implied by the context of odds ratio) is that it represents the change in the log odds of the dependent variable (in this case, the likelihood of being a private school) for a one-unit change in the predictor variable, holding other variables constant. Choice C correctly describes this relationship for a TOEFL criterion of at least 550.

SCENARIO 18-12 The Marketing Manager for a Nationally Franchised Lawn Service Company