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

question 73

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:

Atomic Mass

The mass of an atom, typically expressed in atomic mass units (amu), representing the total number of protons and neutrons in the nucleus.

Covalent Bonds

A chemical bond formed by the sharing of one or more pairs of electrons between atoms.

Phosphorus

A chemical element with the symbol P and atomic number 15, essential to all living cells and used in the manufacture of fertilizers.

Oxygen

A chemical element with symbol O, essential for cellular respiration in most aerobic organisms.