Coefficient of Determination

• Coefficient of determination (r^2) tells us the amount of variation in the dependent variable that can be explained by the variation in the independent variable / by the regression line

• A higher coefficient of determination means that the least squares regression line is more accurate in predicting the DV from the IV.

• When summing residuals we square them first otherwise the positive and negative residuals would all sum to 0

• SS Total = sum (observed - mean)^2

• SS Residual is the exact same thing as SS Total, but the difference is that rather than finding the difference of the values to the mean. We find the sum of the differences of the values compared to the least squares regression line.

• SS Regression is basically SS Total - SS Residual. This is known as the improvement in the prediction resulting from using the regression model rather than the mean.

• The formula of coefficient of determination (r^2) is SS Regression / SS Total

• SPSS shows the SS Total, SS Residual, and SS Regression in the ANOVA table.

SS Total = 476

SS Residual = 140

SS Regression = 335

r^2 = 0.705

Standard Deviation of a Simple Regression Model

• Standard error of estimate = residual standard deviation

• Se = squareroot (SS residual / n - 2 )

• n - 2 because gives a better estimate of the population deviation

• Standard error of estimate is calculated in SPSS and shown in the Model Summary Output as the Std Error of the Estimate