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

question 55

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.
Coefficient Standard Error
X1 0.6251 0.094
X2 0.9210 0.190
X3 -0.5100 0.920
Analysis of Variance
Source of Variation
Degrees of Freedom
Sum of Squares
Mean
Square F
Regression 84
Error 112
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 α = 0.05.
c. At α = 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:

Compounded Monthly

The process of calculating interest on both the initial principal and the accumulated interest of previous periods on a monthly basis.

Semi-Annually

A term referring to an event or action that occurs twice a year.

Quarterly

Occurring every three months or four times a year, often referring to financial reporting or dividend payments.

Increases in Value

Situations or circumstances where the value of an asset, investment, or property rises over time.