If all conditions or assumptions of regression analysis simple regression can give reliable estimates.
The assumptions of regression analysis are:
- Linearity: The relationship between the dependent and independent variables is linear.
- Homoscedasticity: The variance of the errors is constant across all values of the independent variable.
- Normality: The errors are normally distributed.
- Independence: The errors are independent of each other.
- No autocorrelation: The errors are not correlated with each other.
If all of these assumptions are met, then the simple regression model will provide reliable estimates of the relationship between the dependent and independent variables. However, if any of these assumptions are violated, then the simple regression model may not provide reliable estimates.
For example, if the relationship between the dependent and independent variables is not linear, then the simple regression model will not be able to accurately estimate the relationship. Similarly, if the variance of the errors is not constant across all values of the independent variable, then the simple regression model will not be able to accurately estimate the relationship.
Therefore, it is important to check the assumptions of regression analysis before using the simple regression model to make inferences about the relationship between the dependent and independent variables.