Applying the Concepts and Skills Graduation Rates. Graduation rate—the percentage of entering freshmen attending full time and graduating within 5 years— and what influences it is a concern in U.S. colleges and universities. U.S. News and World Report ’s “College Guide” provides data on graduation rates for colleges and universities as a function of the percentage of freshmen in the top 10% of their high school class, total spending per student, and student-to-faculty ratio. A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate). S/F ratio Grad rate S/F ratio Grad rate x y x y 16 45 17 46 20 55 17 50 27 70 17 66 19 50 10 26 22 47 18 60 a. Draw a scatterplot of the data. b. Is finding a regression line for the data reasonable? Explain your answer. c. Determine the regression equation for the data, and draw its graph on the scatterplot you drew in part (a). d. Describe the apparent relationship between student-to-faculty ratio and graduation rate. e. What does the slope of the regression line represent in terms of student-to-faculty ratio and graduation rate? f. Use the regression equation to predict the graduation rate of a university having a student-to-faculty ratio of 17. g. Identify outliers and potential influential observations.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Applying the Concepts and Skills
Graduation Rates. Graduation rate—the percentage of entering freshmen attending full time and graduating within 5 years— and what influences it is a concern in U.S. colleges and universities.
U.S. News and World Report ’s “College Guide” provides data on graduation rates for colleges and universities as a
| S/F ratio | Grad rate | S/F ratio | Grad rate |
| x | y | x | y |
| 16 | 45 |
17 |
46 |
| 20 | 55 | 17 | 50 |
| 27 | 70 | 17 | 66 |
| 19 | 50 | 10 | 26 |
| 22 | 47 | 18 | 60 |
a. Draw a scatterplot of the data.
b. Is finding a regression line for the data reasonable? Explain your answer.
c. Determine the regression equation for the data, and draw its graph on the scatterplot you drew in part (a).
d. Describe the apparent relationship between student-to-faculty ratio and graduation rate.
e. What does the slope of the regression line represent in terms of student-to-faculty ratio and graduation rate?
f. Use the regression equation to predict the graduation rate of a university having a student-to-faculty ratio of 17.
g. Identify outliers and potential influential observations.
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