Using data from 50 workers, a researcher estimates Wage = β0 + β1Education + β2Experience + β3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. The regression results are shown in the following table. Coefficients Standard Error t Stat p-Value Intercept 7.45 3.79 1.97 0.0554 Education 1.06 0.37 2.86 0.0063 Experience 0.37 0.18 2.06 0.0455 Age −0.02 0.06 −0.33 0.7404 a-1. Interpret the point estimate for β1. multiple choice 1 As Education increases by 1 year, Wage is predicted to increase by 1.06/hour. As Education increases by 1 year, Wage is predicted to increase by 0.37/hour. As Education increases by 1 year, Wage is predicted to increase by 1.06/hour, holding Age and Experience constant. As Education increases by 1 year, Wage is predicted to increase by 0.37/hour, holding Age and Experience constant. a-2. Interpret the point estimate for β2. multiple choice 2 As Experience increases by 1 year, Wage is predicted to increase by 1.06/hour. As Experience increases by 1 year, Wage is predicted to increase by 0.37/hour. As Experience increases by 1 year, Wage is predicted to increase by 1.06/hour, holding Age and Education constant. As Experience increases by 1 year, Wage is predicted to increase by 0.37/hour, holding Age and Education constant. b. What is the sample regression equation? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) c. Predict the hourly wage rate for a 40-year-old worker with 3 years of higher education and 2 years of experience. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
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.
Using data from 50 workers, a researcher estimates Wage = β0 + β1Education + β2Experience + β3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. The regression results are shown in the following table.
| Coefficients | Standard Error |
t Stat | p-Value | |
| Intercept | 7.45 | 3.79 | 1.97 | 0.0554 |
| Education | 1.06 | 0.37 | 2.86 | 0.0063 |
| Experience | 0.37 | 0.18 | 2.06 | 0.0455 |
| Age | −0.02 | 0.06 | −0.33 | 0.7404 |
a-1. Interpret the point estimate for β1.
multiple choice 1
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As Education increases by 1 year, Wage is predicted to increase by 1.06/hour.
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As Education increases by 1 year, Wage is predicted to increase by 0.37/hour.
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As Education increases by 1 year, Wage is predicted to increase by 1.06/hour, holding Age and Experience constant.
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As Education increases by 1 year, Wage is predicted to increase by 0.37/hour, holding Age and Experience constant.
a-2. Interpret the point estimate for β2.
multiple choice 2
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As Experience increases by 1 year, Wage is predicted to increase by 1.06/hour.
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As Experience increases by 1 year, Wage is predicted to increase by 0.37/hour.
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As Experience increases by 1 year, Wage is predicted to increase by 1.06/hour, holding Age and Education constant.
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As Experience increases by 1 year, Wage is predicted to increase by 0.37/hour, holding Age and Education constant.
b. What is the sample regression equation? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
c. Predict the hourly wage rate for a 40-year-old worker with 3 years of higher education and 2 years of experience. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
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