Hi Ms. Sue
I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes get it right and wrong most of the time,
to fine error sum of squares, total sums of squares or regression sums of the squares/ can you give me an idea how to find the right one. Thank you
Sorry -- I don't know.
Hello! I'm not Ms. Sue, but I can definitely help you with understanding explained and unexplained variation, as well as finding the error sum of squares, total sum of squares, and regression sum of squares.
Explained Variation:
Explained variation is the variation in the dependent variable (y) that can be accounted for by the independent variable(s) (x). In other words, it measures how well the regression model fits the data. To compute the explained variation, you need to estimate the regression line, and then calculate the sum of squares due to regression (SSR).
Unexplained Variation:
Unexplained variation, also known as the residual variation, is the part of the dependent variable (y) that cannot be explained or accounted for by the independent variable(s) (x). It represents the random fluctuations or errors in the data. To compute the unexplained variation, you need to calculate the sum of squares due to error (SSE).
Total Variation:
Total variation is the total variability in the dependent variable (y). It is the sum of the explained variation and the unexplained variation. To compute the total variation, you need to calculate the sum of squares total (SST).
To determine which sum of squares you need to find (error sum of squares, total sum of squares, or regression sum of squares), you should consider what exactly you want to measure or analyze. Here are the formulas for each:
Error Sum of Squares (SSE):
SSE measures the unexplained variation or the sum of squared residuals. It quantifies the differences between the observed values (y) and the predicted values (ŷ) using the regression line. The formula to find SSE is:
SSE = Σ(y - ŷ)^2
Total Sum of Squares (SST):
SST measures the total variation in the dependent variable (y). It captures both the explained and unexplained variation. The formula to find SST is:
SST = Σ(y - ȳ)^2
Regression Sum of Squares (SSR):
SSR measures the explained variation or the sum of squared deviations between the predicted values (ŷ) and the mean of the dependent variable (ȳ). The formula to find SSR is:
SSR = Σ(ŷ - ȳ)^2
Once you have calculated the relevant sum of squares, you can use these values to assess the goodness of fit of your regression model. The higher the proportion of explained variation (the closer SSR is to SST), the better the regression model fits the data.
Remember, it's important to understand the context of your analysis and what you want to measure in order to choose the appropriate sum of squares.