A multiple regression analysis between yearly income(y in $1,000s), college grade point average(X1) , age of the individuals (X2), and the gender of the individual (X3); zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained. Coefficient Standard Error Constant 4.0928 1.4400 X1 10.0230 1.6512 X2 0.1020 0.1225 X3 -4.4811 1.4400 Analysis of Variance Source of Degrees of Sum of Mean Variance Freedom Squares Square F Regression 360.59 Error 23.91 Write the regression equation for the above. Interpret the meaning of the coefficient of X3. Compute the coefficient of determination.
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 multiple
Coefficient Standard Error
Constant 4.0928 1.4400
X1 10.0230 1.6512
X2 0.1020 0.1225
X3 -4.4811 1.4400
Analysis of Variance
Source of Degrees of Sum of Mean
Variance Freedom Squares Square F
Regression 360.59
Error 23.91
- Write the regression equation for the above.
- Interpret the meaning of the coefficient of X3.
- Compute the coefficient of determination.
- Is the coefficient of X1 significant? Use level of significance=0.05
- Is the coefficient of X2 significant? Use level of significance=0.05
- Is the coefficient of X3 significant? Use level of significance =0.05
- Perform an F test and determine whether or not the model is significant.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
