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

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Presentation transcript:

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

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

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

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

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.

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

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

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’ = x. Find the standard error of estimate. MachineAge x (years)Monthly cost y A162 B278 C370 D490 E493 F6103

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’ = x. Find the standard error of estimate. MachineAge, x (years) Monthly cost, y y’y – y’(y – y’) 2 A162 B278 C370 D490 E493 F6103

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

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’ = x. Find the standard error of estimate. MachineAge, x (years) Monthly cost, y xyy2y2 A162 B278 C370 D490 E493 F6103