An Analyst Has Identified 3 Independent Variables (X₁, X₂, X₃)

question 39

Multiple Choice

An analyst has identified 3 independent variables (X₁, X₂, X₃) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R² value for the X₃ model the same as the R² value for the X₁ and X₃ model, but the Adjusted R² values differ?

• A)The standard error for X₁ is greater than the standard error for X₃.
• B)X₁ does not reduce ESS enough to compensate for its addition to the model.
• C)X₁ does not reduce TSS enough to compensate for its addition to the model.
• D)X₁ and X₃ represent similar factors so multicollinearity exists.

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Definitions:

Isoprene

A common organic compound with the formula C5H8, used as a monomer in the production of natural and synthetic rubbers.

Steroids

A class of lipophilic compounds characterized by a core structure of four fused carbon rings, varying by the functional groups attached and serving in various biological roles.

Sesquiterpene

A class of terpenes that consist of three isoprene units and have the molecular formula C15H24.

Steroid

A type of organic molecule with a characteristic molecular structure containing four rings of carbon atoms (three six-membered and one five-membered).