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

question 54

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 Excel output 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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