Does the regression line equation change if you change the independent and dependent variable
The equation doesn't change, just the values.
So it will change the values that are being manipulated
Yes, the regression line equation does change if you change the independent and dependent variables in a regression analysis. The regression line equation represents the relationship between the independent variable(s) and the dependent variable, and it is derived using a specific set of variables.
To explain how to get the regression line equation, let's consider a simple linear regression, which involves one independent variable and one dependent variable.
1. Collect data: Gather a set of paired observations for the independent variable (X) and the dependent variable (Y). Each observation should have an X value and its corresponding Y value.
2. Plot the data: Create a scatter plot with the X values on the x-axis and the Y values on the y-axis. This will help visualize the relationship between the variables.
3. Fit the regression line: Use statistical software or methods to calculate the best-fit line that minimizes the difference between the observed Y values and the predicted Y values based on the X values. This line is typically known as the "regression line" or "line of best fit."
4. Interpret the equation: The equation of the regression line can be written in the form of: Y = a + b*X, where Y is the dependent variable, X is the independent variable, "a" is the y-intercept (the value of Y when X is 0), and "b" is the slope of the line.
If you change the independent and dependent variables in your analysis, you need to repeat these steps with the new variables to obtain the correct regression line equation. The analysis and equations are specific to the variables included in the analysis, and changing the variables will result in a different equation that represents the relationship between the new variables.