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:

Future Value

The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.

Interest

The cost of borrowing money, often expressed as a percentage of the amount borrowed, paid to the lender over a specified period.

Time-Value

The concept that money available at the present time is worth more than the same amount in the future due to its potential earning capacity.

Money

Any item that is generally acceptable to sellers in exchange for goods and services.