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

question 86

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:

Units of Variable K

In economics, this refers to units of a variable factor of production (K often denotes capital), where the quantity can be changed in the short run to increase or decrease production.

Units of Output

The quantity of goods or services produced by an entity in a given period of time.

Marginal Cost

The cost associated with producing an additional unit of a product or service.

Diminishing

Refers to a reduction or decrease over time.