If the total sum of squares (TSS) in a regression equation is 81, and the residual sum of squares (RSS) is 25, what is the explained sum of squares (ESS)? A) 32 B) 56 C) 64 D) 18
Added by Alba W.
Step 1
The total sum of squares (TSS) is the total variation in the dependent variable, and it can be decomposed into the explained sum of squares (ESS) and the residual sum of squares (RSS). The relationship is given by the formula: \[ \text{TSS} = \text{ESS} + Show more…
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4.9. A three-variable regression gave the following results: Source of variation | Sum of squares (SS) | d.f. | Mean sum of squares (MSS) Due to regression (ESS) | 65,965 | — | — Due to residual (RSS) | — | — | — Total (TSS) | 66,042 | 14 | — a. What is the sample size? b. What is the value of the RSS? c. What are the d.f. of the ESS and RSS? d. What is R²? And Ŕ²? e. Test the hypothesis that X₂ and X₃ have zero influence on Y. Which test do you use and why? f. From the preceding information, can you determine the individual contribution of X₂ and X₃ toward Y?
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