10.3 Coefficient of Determination and Standard Error of the Estimate By the end of class you will be able to calculate the coefficient of determination and standard error of the estimate.

Investigation: Tile/Cutting Cost

Vocabulary: Explained Variation: The variation obtained from the actual relationship between the independent and dependent variables x and y. Recall y prime is the predicted value on the regression line. Formula:

Unexplained Variation: Unexplained Variation: The variation due to chance. Y is the actual value for x, not the predicted value on the regression line. Formula:

Total Variation TV = Explained Variation + Unexplained Variation Formula:

Residual The difference between the actual point (x, y) and the point on the regression line (x, y’). The sum of the residuals computed by using the regression line is the smallest possible value, which is why the regression line is called the least-squares line.

Residual Plot X axis: x values Y axis: residuals When residuals are evenly distributed about a line predictions can be made.

(a) Regression line can be used to make predictions (the red line is not the regression line-is the mean of the residuals)

Coefficient of Determination Ratio of the explained variation to the total variation Can get from calculator LinReg Formula: Coefficient of Nondetermination is

Standard Error of the Estimate The standard deviation of the observed y values about the predicted y values (the closer observed values are to the predicted, the smaller this is) Measures how data points (actual) deviate from the regression line. Formula:

Graph the regression line Graph the residual plot Copy Machine Age vs. Monthly Maintenance Costs (1, $62) (2, $78) (3, $70) (4, $90) (4, $93) (6, $103) Create a scatterplot Graph the regression line Graph the residual plot Find the Explained Variation Find the Unexplained Variation Find the Total Variation Find the Coefficient of Determination Find the Standard Error of the Estimate