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.

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Presentation transcript:

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.

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

PREDICTION ERROR

Sum of Squares Error (SSE)

Standard Error of the Estimate, s

Total Sum of Squares, SST

Sum of Squares Regression, SSR

Combined Relationship SST = SSR + SSE

Coefficient of Determination, r 2

Data Set Volume, xWeights, y

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

Data Set Volume x Weights y

Data Set Volume x Weights y To find the predicted score we have to find the regression line using our calculators. y = x (-0.4) (-0.8) 2 (1.8) 2 (0.4) 2 (-1) (-13.2) 2 (-7.2) 2 (1.8) 2 (6.8) 2 (11.8) ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) SSR SST SSE

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)