Multiple Regression Analysis Was Used to Study How an Individual's $\alpha$

question 2

Essay

Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X₁ in years), level of education (X₂ ranging from 1 to 5), and the person's gender (X₃ where 0 =female and 1=male). The following is a partial result of a computer program that was used on a sample of 20 individuals.
a.Compute the coefficient of determination.
b.Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., X₂) is significantly different from zero. Let $\alpha$ = 0.05.
c.At $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant.
d.As you note the coefficient of X₃ is -0.510. Fully interpret the meaning of this coefficient.

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Definitions:

Deadweight Loss

Economic inefficiency resulting when the market equilibrium for a good or a service is not achieved.

Social Cost

The total cost to society, including both private costs and any external costs, from producing or consuming a good or service.

Total Surplus

The sum of consumer surplus and producer surplus in a market, representing the total net benefit to society.

Social Welfare

A set of government programs aimed at providing support to the needy in society, ensuring a minimum standard of living and protection against economic risks.