What is simple regression analysis, explain its components?
Simple regression analysis is a statistical method used to understand the relationship between two variables. It involves examining the relationship between a dependent variable, denoted as Y, and an independent variable, denoted as X.
The components of a simple regression analysis include:
1. Dependent variable (Y): This is the variable that you are trying to predict or understand. It is also known as the outcome variable or response variable.
2. Independent variable (X): This is the variable that is believed to have an effect on the dependent variable. It is also known as the predictor variable or explanatory variable.
3. Regression equation: The equation that relates the dependent variable to the independent variable is known as the regression equation. It is represented as Y = b0 + b1*X, where b0 is the intercept and b1 is the slope of the regression line.
4. Slope (b1): The slope of the regression line indicates the strength and direction of the relationship between the independent and dependent variables. It shows how much the dependent variable changes for a one-unit change in the independent variable.
5. Intercept (b0): The intercept is the value of the dependent variable when the independent variable is zero. It represents the value of the dependent variable when the independent variable has no effect.
6. Residuals: Residuals are the differences between the observed values of the dependent variable and the predicted values from the regression equation. They can be used to measure the accuracy of the regression model.
Overall, simple regression analysis helps in understanding and making predictions about the relationship between two variables based on the data available.