Multiple Regression Analysis Was Used to Study the Relationship Between $\beta$

question 40

Essay

Multiple regression analysis was used to study the relationship between a dependent variable, Y, and three independent variables X₁, X₂ and, X₃. The following is a partial result of the regression analysis involving 20 observations.

a.Compute the coefficient of determination.
b.Perform a t test and determine whether or not $\beta$ ₁ is significantly different from zero ( $\alpha$ = 0.05).
c.Perform a t test and determine whether or not $\beta$ ₂ is significantly different from zero ( $\alpha$ = 0.05).
d.Perform a t test and determine whether or not $\beta$ ₃ is significantly different from zero ( $\alpha$ = 0.05).
e.
At $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant.

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Definitions:

Nucleic Acid

Macromolecules essential for all known forms of life, including DNA and RNA, which store and transfer genetic information.

Carbohydrate

Class of organic compounds that typically contain carbon, hydrogen, and oxygen in a 1:2:1 ratio; includes the monosaccharides, disaccharides, and polysaccharides.

Hydrolysis

A chemical reaction involving the breaking of a bond in a molecule using water, common in the digestion of nutrients.

Fatty Acids

Long-chain hydrocarbons found in fats and oils, serving as major sources of energy, components of cell membranes, and precursors for bioactive signaling molecules.