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4.4 Further Topics in Regression Analysis

4.4 Further Topics in Regression Analysis. Objectives: By the end of this section, I will be able to… Explain prediction error, calculate SSE, and utilize the standard error s as a measure of a typical prediction error.

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4.4 Further Topics in Regression Analysis

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  1. 4.4 Further Topics in Regression Analysis Objectives: By the end of this section, I will be able to… Explain prediction error, calculate SSE, and utilize the standard error sas a measure of a typical prediction error. Describe how total variability, prediction error, and improvement are measured by SST, SSE, and SSR. Explain the meaning of r2 as a measure of the usefulness of the regression.

  2. Regression Analysis Analysts use correlation and linear regression to analyze a data set. They also look at the data and determine “errors”.

  3. PREDICTION ERROR Measures how far the predicted value, is from the actual value, y, observed in the data set.

  4. Sum of Squares Error (SSE) All the prediction errors are squared and then added up.

  5. Standard Error of the Estimate, s A measure of the size of the typical prediction error.

  6. Total Sum of Squares, SST A measure of the total variability in the values of the y variable.

  7. Sum of Squares Regression, SSR Measures the amount of improvement in the accuracy of our estimates when using the regression equation compared with relying only on the y values and ignoring the x information.

  8. Combined Relationship SST = SSR + SSE

  9. Coefficient of Determination, r2 Measures the goodness of fit of the regression equation to the data. It is the ratio of SSR/SST. Is between 0 and 1.

  10. Data Set

  11. Find the following values • Regression Line • r • SSE • s • SSR • SST • r2

  12. Data Set

  13. Data Set 10.4 10-10.4 -0.4 To find the predicted score we have to find the regression line using our calculators. (-0.4)2 0.16 -13.2 10-23.2 174.24 (-13.2)2 163.84 (10.4-23.2)2 40.96 16-23.2 -7.2 51.84 16.8 (-7.2)2 (16.8-23.2)2 16-16.8 -0.8 (-0.8)2 0.64 3.24 23.2 1.8 25-23.2 (1.8)2 1.8 (1.8)2 25-23.2 3.24 0 (23.2-23.2)2 y = 4 + 1.6x 29.6 30-23.2 (6.8)2 46.24 6.8 0.4 30-29.6 (0.4)2 0.16 (29.6-23.2)2 40.96 35-36 (-1)2 36 -1 1 163.84 35-23.2 11.8 139.24 (11.8)2 (36-23.2)2 SSE 5.2 SST 414.8 409.6 SSR

  14. Regression Line, r, and r2 were found on calculator. There is only one left to find… 1.316561177

  15. Time to get a Program! • Then find the following values for the data set. • Regression Line • r • SSE • s • SSR • SST • r2

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