Question

A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT) at the university or college and whether the TOEFL criterion is at least 90 (Toefl90 1 if yes, 0 otherwise). The PHStat output is given below: Referring to Table 14-18, which of the following is the correct interpretation for the Toefi90 slope coefficient? Holding constant the effect of SAT, the estimated mean value of school type is 0.1928 higher when the school has a TOEFL criterion that is at least 90. Holding constant the effect of SAT, the estimated school type increases by 0.1928 when the school has a TOEFL criterion that is at least 90. Holding constant the effect of SAT, the estimated natural logarithm of the odds ratio of the school being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not. Holding constant the effect of SAT, the estimated probability of the school being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not.

Answer 1

The correct option is as follows;

Holding constant the effect of SAT, the estimated probability of being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not

Explanation:

Here we have from the question, the significant level criterion is set at TOEFL criterion of 90. We therefore test the hypothesis using a 90% confidence level such that our α = 1 - 0.9 = 0.1

From the the table data therefore, given that 1 represent private school and 0 otherwise, the only predictor with a p-Value > our α is the TOEFL90 :1, that is p-Value of TOEFL90 :1 = 0.7407 > 0.1

Therefore, on comparison with the options, the most correct option is as follows;

Holding constant the effect of SAT, the estimated probability of being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not.