A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary Education 34 3 66 1 ⋮ ⋮ 33 0 Click here for the Excel Data File a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.) Salaryˆ=Salary^= + Education b. Interpret the coefficient for Education. multiple choice As Education increases by 1 year, an individual’s annual salary is predicted to increase by $4,690. As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $4,690. As Education increases by 1 year, an individual’s annual salary is predicted to increase by $8,590. As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $8,590. c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.) SalaryˆSalary^ $
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.
A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:
| Salary | Education | ||||
| 34 | 3 | ||||
| 66 | 1 | ||||
| ⋮ | ⋮ | ||||
| 33 | 0 | ||||
Click here for the Excel Data File
a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.)
Salaryˆ=Salary^= + Education
b. Interpret the coefficient for Education.
multiple choice
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As Education increases by 1 year, an individual’s annual salary is predicted to increase by $4,690.
-
As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $4,690.
-
As Education increases by 1 year, an individual’s annual salary is predicted to increase by $8,590.
-
As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $8,590.
c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)
SalaryˆSalary^ $
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