2. 4.4 4.4 Further Topics in Regression Analysis Objectives: By the end of this section, I will be able to… 1) Explain prediction error, calculate SSE, and utilize the standard error s as a measure of a typical prediction error. 2) Describe how total variability, prediction error, and improvement are measured by SST, SSE, and SSR. 3) Explain the meaning of r 2 as a measure of the usefulness of the regression.

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

4. PREDICTION ERROR

5. Sum of Squares Error (SSE)

6. Standard Error of the Estimate, s

7. Total Sum of Squares, SST

8. Sum of Squares Regression, SSR

9. Combined Relationship SST = SSR + SSE

10. Coefficient of Determination, r 2

11. Data Set Volume, xWeights, y 410 816 1225 1630 2035

12. Find the following values 1. R egression Line 2. r 3. S SE 4. s 5. S SR 6. S ST 7. r 2

13. Data Set Volume x Weights y 410 816 1225 1630 2035

14. Data Set Volume x Weights y 410 816 1225 1630 2035 To find the predicted score we have to find the regression line using our calculators. y = 4 + 1.6x 10.4 16.8 23.2 29.6 36 10-10.4-0.4 16-16.8 -0.8 (-0.4) 2 0.16 (-0.8) 2 (1.8) 2 (0.4) 2 (-1) 2 0.64 3.24 0.16 1 10-23.2-13.2 16-23.2 25-23.2 -7.2 1.8 (-13.2) 2 (-7.2) 2 (1.8) 2 (6.8) 2 (11.8) 2 174.24 51.84 3.24 46.24 139.24 (10.4-23.2) 2 (16.8-23.2) 2 (23.2-23.2) 2 (29.6-23.2) 2 (36-23.2) 2 163.84 40.96 0 163.84 SSR SST SSE5.2 414.8409.6 25-23.2 30-29.6 30-23.2 35-23.2 35-36 1.8 6.8 11.8 0.4

16. Time to get a Program!  Then find the following values for the data set. data setdata set 1. Regression Line 2. r 3. SSE 4. s 5. SSR 6. SST 7. r 2 HEIGHTS (in inches) HAND LENGTH (in inches)