A Multiple Linear Regression Analysis Involving 45 Observations Resulted in the Following

question 47

Essay

A multiple linear regression analysis involving 45 observations resulted in the following least squares prediction equation: $$\hat { y } = .408 + 1.3387 x _ { 1 } + 2.1 x _ { 2 }$$ .
The SSE for the above model is 49.
Addition of two other independent variables to the model,resulted in the following multiple linear regression equation: $$\hat { y } = 1.2 + 3 x _ { 1 } + 12 x _ { 2 } + 4 x _ { 3 } + 8 x _ { 4 }$$ .
The latter model's SSE is 40.
-Determine the degrees of freedom regression (explained variation),degrees of freedom error (unexplained variation),and total degrees of freedom for the latter model (the model with four independent variables).

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Definitions:

Coefficient of Variation

A standardized measure of dispersion of a probability distribution or frequency distribution, expressed as a percentage of the mean.

Ether

A class of organic compounds characterized by an oxygen atom connected to two alkyl or aryl groups; they are often used as solvents.

Molecule

The smallest particle of a chemical element or compound that has the chemical properties of that element or compound.

1,2-dibromoethene

A halogenated alkene with the formula C2H2Br2, characterized by having two bromine atoms attached to adjacent carbon atoms in the ethene molecule.