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

question 43

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:

Par Value

The face value of a security as stated by the issuing company, which may or may not reflect its market value.

Stockholders' Equity

The residual interest in the assets of a corporation that remains after deducting its liabilities.

Book Value Per Share

The equity available to common shareholders divided by the number of outstanding shares.

Dividends

Payments made by a corporation to its shareholder members, representing a portion of the corporate profits distributed among shareholders.