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)
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