2. what is simple regression analysis, explain its components ?
Simple regression analysis is a statistical method used to establish a relationship between two variables - a dependent variable and an independent variable. It is used to analyze how the value of the dependent variable changes when the independent variable is changed.
Components of simple regression analysis:
1. Dependent variable: This is the variable that is being predicted or explained in the analysis. It is denoted by Y.
2. Independent variable: This is the variable that is influencing or determining the value of the dependent variable. It is denoted by X.
3. Regression equation: This is the mathematical equation that represents the relationship between the independent and dependent variables. It is in the form of Y = a + bX, where a is the intercept of the line and b is the slope of the line.
4. Residuals: Residuals are the differences between the observed values of the dependent variable and the predicted values from the regression equation. A good regression model will have small residuals, indicating a good fit.
5. Coefficient of determination (R-squared): This is a measure of how well the regression model fits the data. It ranges from 0 to 1, with 1 indicating a perfect fit.
6. Coefficients: The coefficients of the regression equation (a and b) determine the intercept and slope of the regression line, respectively. They provide information on how the dependent variable changes with changes in the independent variable.
Overall, simple regression analysis helps to understand the relationship between two variables and make predictions based on that relationship.