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

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

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

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  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 r2 r2 = explained variation total variation - r2 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: x 1 2 3 4 5 y 10 8 12 16 20 - r = 0.919 - therefore, r2 = 0.845 • To find the coefficient of nondetermination 1 - r2 = 1 - .845 = 0.155

  5. Relationship between r and r2 • As the value of r approaches 0, r2 decreases more rapidly Example: - If r = 0.6, then r2 = 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.

  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.

  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.

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