1. Aim: How do we compute the coefficients of determination and the standard error of estimate?

2. Coefficient of Determination Coefficient of Determination: the ratio of the explained variation to the total variation –Denoted by r 2 r 2 = explained variation total variation - r 2 is usually expressed as a percentage

3. Coefficient of Nondetermination The coefficient of determination gives a measure of the variation of the dependent; usually expressed as a percentage –Therefore…the remaining of the percentage to equal a total of 100% is the value of the coefficient of nondetermination

4. Fastest way to find coefficient of determination Find the correlation coefficient (r) and square that answer Example: x12345 y 108121620 - r = 0.919 - therefore, r 2 = 0.845 -To find the coefficient of nondetermination 1 - r 2 = 1 -.845 = 0.155

5. Relationship between r and r 2 As the value of r approaches 0, r 2 decreases more rapidly Example: - If r = 0.6, then r 2 = 0.36, which means that only 36% of the variation in the dependent variable can be attributed to the variation in the independent variable.

6. Standard Error of the Estimate Standard Error of the Estimate: the standard deviation of the observed y values about the predicted y’ values –The prediction interval –The closer the observed values are to the predicted values, the smaller the standard error of the estimate

7. Computing the standard error y = observed value y’ = predicted value n = total number of data

8. Example: A researcher collects the following data and determines that there is a significant relationship between the age of a copy machine and its monthly maintenance cost. The regression equation is y’ = 55.57 + 8.13x. Find the standard error of estimate. MachineAge x (years)Monthly cost y A162 B278 C370 D490 E493 F6103

9. Example Continued A researcher collects the following data and determines that there is a significant relationship between the age of a copy machine and its monthly maintenance cost. The regression equation is y’ = 55.57 + 8.13x. Find the standard error of estimate. MachineAge, x (years) Monthly cost, y y’y – y’(y – y’) 2 A162 B278 C370 D490 E493 F6103

10. If preferred… The standard error of the estimate can be found by using the formula a and b are the coefficient of the regression line n = total number of data

11. Same example: Different formula A researcher collects the following data and determines that there is a significant relationship between the age of a copy machine and its monthly maintenance cost. The regression equation is y’ = 55.57 + 8.13x. Find the standard error of estimate. MachineAge, x (years) Monthly cost, y xyy2y2 A162 B278 C370 D490 E493 F6103