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B. The Analysis of Variance provides the basis for summarizing the decomposition

ID: 3317019 • Letter: B

Question

B. The Analysis of Variance provides the basis for summarizing the decomposition of the variation of the dependent variable from the mean. Part of this variation is explained by the regression (SSE), and part of it is unexplained (SSR). Thus the total variation (SST) is related to the other variations as follows:   SST = SSE + SSR   ……   (4)

Analysis of Variance Table

Source                                         Sum of Squares                Degree of Freedom      Mean Square      

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                       Explained                                     SSE = 25221.2229              1                                    SSE/1 =25221.2229

                       Unexplained                               SSR = 54311.3314           38                                 SSR/38 =1429.2455

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                       Total                                        SST= 79532.5544            39

Divide equation (4) above by SST and write out the equation. Then interpret the new equation.

Calculate the proportion of the total variation explained by the regression. What is the statistical name of the value you have calculated?

Please show me the answers step by step

Explanation / Answer

ANSWER:

The proportion of the total variation explained by the regression is calculated by using coefficient of determination and it is denoted by R2. It is defined by

R2 = (SSR/SST) = (54311.3314/79532.5544) = 0.6829

R2 = 0.6829 = 68.29%

i.e. 68.29% of the total variation explained by the regression.

The statistical name: Coefficient of determination (R2)