Determine whether there is a significant linear relationship. Each year U.S. News and World Report conducts its "Survey of America's Best Graduate and Professional Schools." and ranks the top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate. 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. An 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. The results of a simple linear regression of SALARY versus GMAT using the 25 data points are shown below. Is there sufficient evidence to suggest there is a linear relationship between SALARY and GMAT at the 5% level of significance? ----------------------------------------------------------------------------------- a = -92040 b = 228 s = 3213 r 2 = .66 r = .81 df = 23 t = 6.67 (the test statistic) ----------------------------------------------------------------------------------- State your conclusion. a) There is enough evidence (at α = .05) to suggest that there is a linear relationship between SALARY and GMAT. b) Only 6.67% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. c) There is not enough evidence (at α = .05) of at least a positive linear relationship between SALARY and GMAT. d) We estimate SALARY to increase $6.67 for every 1-point increase in GMAT
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.
Determine whether there is a significant linear relationship.
Each year U.S. News and World Report conducts its "Survey of America's Best Graduate and
Professional Schools." and ranks the top 25 business schools, as determined by reputation, student
selectivity, placement success, and graduation rate.
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.
An 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. The results of a simple linear regression of
SALARY versus GMAT using the 25 data points are shown below. Is there sufficient evidence to
suggest there is a linear relationship between SALARY and GMAT at the 5% level of significance?
-----------------------------------------------------------------------------------
a = -92040 b = 228 s = 3213 r
2 = .66 r = .81 df = 23 t = 6.67 (the test statistic)
-----------------------------------------------------------------------------------
State your conclusion.
a) There is enough evidence (at α = .05) to suggest that there is a linear relationship between SALARY
and GMAT.
b) Only 6.67% of the sample variation in SALARY can be explained by using GMAT in a straight-line
model.
c) There is not enough evidence (at α = .05) of at least a positive linear relationship between SALARY
and GMAT.
d) We estimate SALARY to increase $6.67 for every 1-point increase in GMAT
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