Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the person's gender (X3 where 1 =female and 0=male). The following is a partial result of a computer program that was used on a sample of 30 individuals. Coefficient Standard Error X1 0.63 0.094 X2 0.94 0.190 X3 0.52 0.120 Analysis of Variance Source of Degrees Sum of Mean Variation of Freedom Squares Square F Regression 90 Error 100 Use the above results and write the regression equation that can be used to predict income. If the individual is 45 years old, level of education is 4, and the person ‘s gender is male ,what is your estimate of income ? Give your answer in dollars. Compute the coefficient of determination and interpret its meaning.
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.
Multiple
Coefficient Standard Error
X1 0.63 0.094
X2 0.94 0.190
X3 0.52 0.120
Analysis of Variance
Source of Degrees Sum of Mean
Variation of Freedom Squares Square F
Regression 90
Error 100
- Use the above results and write the regression equation that can be used to predict income.
- If the individual is 45 years old, level of education is 4, and the person ‘s gender is male ,what is your estimate of income ? Give your answer in dollars.
- Compute the coefficient of determination and interpret its meaning.
- Compute the adjusted coefficient of determination and explain the difference if any between R² and R²ad .
- Perform a t test and determine whether or not the coefficients of regressions are significantly different from zero. Let a = 0.05.
- At a = 0.05, perform an F test and determine whether or not the regression model is significant.
- Fully interpret the meaning of the coefficients of regression .
- Based on F-test, T-test and R² how well this model fits to this situation
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