Graduation Rates. regarding the relationship between college graduation rate and the predictor variables student-to-faculty ratio, percentage of freshmen in the top 10% of their high school class, and percentage of applicants accepted. a. At the 5% significance level, do the data provide sufficient evidence to conclude that percentage of freshmen in the top 10% of their high school class is useful for predicting graduation rate? Be precise in your conclusion. b. Repeat part (a) for each of the variables student-to-faculty ratio and percentage accepted. c. Do you think another regression analysis is called for? If so, which predictor variable(s) might you include? Explain your answers. d. Find a 95% confidence interval for the coefficient β2 of the predictor variable x2 (percentage of freshmen in the top 10% of their high school class). e. Interpret your result from part (d) in words. f. Repeat part (d) for the coefficient β1 of the predictor variable x1 (student-to-faculty ratio).
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.
Graduation Rates. regarding the relationship between college graduation rate and the predictor variables student-to-faculty ratio, percentage of freshmen in the top 10% of their high school class, and percentage of applicants accepted.
a. At the 5% significance level, do the data provide sufficient evidence to conclude that percentage of freshmen in the top 10% of their high school class is useful for predicting graduation rate? Be precise in your conclusion.
b. Repeat part (a) for each of the variables student-to-faculty ratio and percentage accepted.
c. Do you think another
d. Find a 95% confidence interval for the coefficient β2 of the predictor variable x2 (percentage of freshmen in the top 10% of their high school class).
e. Interpret your result from part (d) in words.
f. Repeat part (d) for the coefficient β1 of the predictor variable x1 (student-to-faculty ratio).
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