Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. School GMAT Acc. Rate Salary Harvard 644 15.0% $ 63,000 Stanford 665 10.2 60,000 Penn 644 19.4 55,000 Northwestern 640 22.6 54,000 MIT 650 21.3 57,000 Chicago 632 30.0 55,269 Duke 630 18.2 53,300 Dartmouth 649 13.4 52,000 Virginia 630 23.0 55,269 Michigan 620 32.4 53.300 Columbia 635 37.1 52,000 Cornell 648 14.9 50,700 CMU 630 31.2 52,050 UNC 625 15.4 50,800 Cal-Berkeley 634 24.7 50,000 UCLA 640 20.7 51,494 Texas 612 28.1 43,985 Indiana 600 29.0 44,119 NYU 610 35.0 53,161 Purdue 595 26.8 43,500 USC 610 31.9 49,080 Pittsburgh 605 33.0 43,500 Georgetown 617 31.7 45,156 Maryland 593 28.1 42,925 Rochester 605 35.9 44,499 The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. Conduct a simple linear regression of SALARY versus GMAT using the 25 data points in the table. Find the least squares equation for the model. Use excel to conduct data analysis. Provide detailed interpretation of the results.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student.
School GMAT Acc. Rate Salary
- Harvard 644 15.0% $ 63,000
- Stanford 665 10.2 60,000
- Penn 644 19.4 55,000
- Northwestern 640 22.6 54,000
- MIT 650 21.3 57,000
- Chicago 632 30.0 55,269
- Duke 630 18.2 53,300
- Dartmouth 649 13.4 52,000
- Virginia 630 23.0 55,269
- Michigan 620 32.4 53.300
- Columbia 635 37.1 52,000
- Cornell 648 14.9 50,700
- CMU 630 31.2 52,050
- UNC 625 15.4 50,800
- Cal-Berkeley 634 24.7 50,000
- UCLA 640 20.7 51,494
- Texas 612 28.1 43,985
- Indiana 600 29.0 44,119
- NYU 610 35.0 53,161
- Purdue 595 26.8 43,500
- USC 610 31.9 49,080
- Pittsburgh 605 33.0 43,500
- Georgetown 617 31.7 45,156
- Maryland 593 28.1 42,925
- Rochester 605 35.9 44,499
The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. Conduct a simple linear regression of SALARY versus GMAT using the 25 data points in the table. Find the least squares equation for the model. Use excel to conduct data analysis. Provide detailed interpretation of the results.
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