The distance between the Y value in the data and the Y value predicted from the regression equation is known as the residual. What is the value for the sum of the squared residuals?
SSresidual = r2(SSX)
SSresidual = (1 – r2)(SSX)
SSresidual = r2(SSY)
SSresidual = (1 – r2)(SSY)
To find the value for the sum of the squared residuals (SSresidual), you can use the formula SSresidual = (1 – r^2)(SSY), where r^2 is the coefficient of determination (also known as the R-squared value) and SSY is the sum of squares total.
Here are the steps to calculate SSresidual using the formula:
1. Calculate the coefficient of determination (r^2) from the regression analysis. This value represents the proportion of the total variation in the dependent variable (Y) that is explained by the independent variable (X). The formula for r^2 is typically provided in the output of the regression analysis.
2. Calculate the sum of squares total (SSY), which represents the total variation in the dependent variable (Y) around its mean. This can be calculated using the formula SSY = Σ(Yi - Ȳ)^2, where Yi is the actual value of Y and Ȳ is the mean of Y.
3. Substitute the calculated values of r^2 and SSY into the formula SSresidual = (1 – r^2)(SSY).
By following these steps and plugging in the appropriate values, you can find the value for the sum of the squared residuals (SSresidual).